Rozprawy doktorskie na temat „NONLINEAR STRAINS”

The control of stresses and liquid pressure surges in pipes is an important problem in the design of hydraulic pipe networks. The method of characteristics has been used to solve the transient stresses and pressures in liquid-filled piping systems. The friction force is included in the equations of motion for the fluid and the pipe wall. The maximum pressure and maximum stress at any point along the length of the pipe are evaluated for the entire simulation time. A nonlinear search technique has been developed using the simplex method. The optimal valve closure is sought, that will minimize the maximum pressure and/or stresses. A continuous optimal valve closure policy is specified using spline functions. Numerical examples are presented showing the reduction of the dynamic pressure and the dynamic stress from linear valve closure to optimal valve closure for a simple pipeline and a complex pipeline. Also, a method for choosing the shortest time of closure which will keep the stresses below specified allowable stresses is presented.

In this paper we discuss the inverse problem of the identification of mechanical stresses by measuring the deformation of an electric potential field in a so called differential strain gauge (D-DMS). We derive a mathematical model, where the forward operator is given in terms of an elliptic boundary value problem. Derivatives of the forward operator are considered and the solution of the inverse problem via a least-squares minimization is introduced. Here, the discretized problem is solved with the Gauss-Newton method. Numerical studies of practical interest are presented.

The research work presented here deals with the problems of geometrically nonlinear analysis of thin shell structures. The specific objective was to develop geometrically nonlinear formulations, using Discrete-Kirchhoff Curved Triangular (DKCT) thin shell elements. The DKCT elements, formulated in the natural curvilinear coordinates, based on arbitrary deep shell theory and representing explicit rigid body modes, were successfully applied to linear elastic analysis of composite shells in an earlier research work. A detailed discussion on the developments of classical linear and nonlinear shell theories and the Finite Element applications to linear and nonlinear analysis of shells has been presented. The difficulties of developing converging shell elements due to Kirchhoff's hypothesis have been discussed. The importance of formulating shell elements based on deep shell theory has also been pointed out. The development of shell elements based on Discrete-Kirchhoff's theory has been discussed. The development of a simple 3-noded curved triangular thin shell element with 27 degrees-of-freedom in the tangent and normal displacements and their first-order derivatives, formulated in the natural curvilinear coordinates and based on arbitrary deep shell theory, has been described. This DKCT element has been used to develop geometrically nonlinear formulation for the nonlinear analysis of thin shells. A detailed derivation of the geometrically nonlinear (GNL) formulation, using the DKCT element based on the Total Lagrangian approach and the principles of virtual work has been presented. The techniques of solving the nonlinear equilibrium equations, using the incremental methods has been described. This includes the derivation of the Tangent Stiffness matrix. Various Newton-Raphson solution algorithms and the associated convergence criteria have been discussed in detail. Difficulties of tracing the post buckling behavior using these algorithms and hence the necessity of using alternative techniques have been mentioned. A detailed numerical evaluation of the GNL formulation has been carried out by solving a number of standard problems in the linear buckling and GNL analysis. The results compare well with the standard solutions in linear buckling cases and are in general satisfactory for the GNL analysis in the region of large displacements and small rotations. It is concluded that this simple and economical element will be an ideal choice for the expensive nonlinear analysis of shells. However, it is suggested that the element formulation should include large rotations for the element to perform accurately in the region of large rotations.

Doutoramento em Engenharia Mecânica
In the present work, finite strain elastoplastic constitutive formulations suitable for advanced metallic materials are developed. The main goals are the correct description of the elastoplastic behaviour, including strong plastic anisotropy and cyclic hardening phenomena, in the large strain regime, as well as the development of numerically efficient algorithmic procedures for numerical implementation of the constitutive models into codes of numerical simulation by the Finite Element Method. Two different approaches are used in the derivation of the finite strain constitutive formulations, namely, hypoelasticity and hyperelasticity. On the one hand, regarding the hypoelastic-based model, particular attention is given to the development of computationally effcient forward- and backward-Euler algorithms considering distinct techniques. On the other hand, concerning the hyperelastic-based model, the focus is on the possibility of using any (quadratic or nonquadratic) yield criteria and on a new procedure that ensures that the anisotropy is correctly described in the finite strain regime. Moreover, the constitutive relations are solely expressed in the reference configuration, hence yielding symmetric tensor-valued quantities only. This symmetry, allied to an algorithm that preserves it, is crucial for the computational efficiency of the model's implementation since it reduces the storage effort and the required solver capacities when compared to the model's standard counterparts. For a better description of cyclic hardening phenomena, the developed models and corresponding algorithms, are extended to include several back stresses. This extension is carried out by considering a modified rheological model of nonlinear kinematic hardening and using additional state variables. The capabilities of the developed models for accurate reproduction of the plastic anisotropy and cyclic hardening phenomena are assessed by means of their implementation into material user subroutines of the commercial code Abaqus. The accuracy and computational efficiency of the models and numerical algorithms are compared by means of simulations of benchmarks. These benchmarks allow the models' assessment in the description of, e.g., metal forming defects such as earing and springback, as well as the comparison of the stability and precision of the numerical algorithms.
No presente trabalho, são desenvolvidas formulações constitutivas elastoplásticas para grandes deformações, adequadas a materiais metálicos avançados. Os principais objectivos deste estudo consistem na correcta descrição do comportamento elastoplástico, incluindo anisotropia plástica acentuada e fenómenos de endurecimento cíclico, no regime de grandes deformações, bem como o desenvolvimento de procedimentos algorítmicos eficientes para a implementação numérica dos modelos constitutivos em códigos de simulação numérica pelo Método dos Elementos Finitos. São usadas duas metodologias diferentes na derivação das formulações constitutivas de grandes deformações, nomeadamente, hipoelasticidade e hiperelasticidade. Por um lado, relativamente ao modelo baseado em hipoelasticidade, é dada particular atenção ao desenvolvimento de algoritmos eficientes do ponto de vista computacional, considerando técnicas particulares. Por outro lado, em relação ao modelo baseado em hiperelasticidade, a possibilidade de usar qualquer critério de cedência (quadrático ou não-quadrático) e a apresentação de um procedimento inovador, que garante a correcta descrição da anisotropia na presença de grandes deformaçães, são destacadas. Além disso, as relações constitutivas são expressas unicamente na configuração de referência, resultando no uso de apenas variáveis simétricas de segunda ordem. Esta simetria e o uso de um algoritmo que a preserva são cruciais no que diz respeito à eficiência numérica da implementação do modelo, uma vez que reduz significativamente o espaço de armazenamento e o custo computacional de cálculo, relativamente aos modelos hiperelásticos convencionais. Os modelos, e respectivos algoritmos de integração, são posteriormente alargados ao uso de múltiplos tensores das tensões inversas de modo a permitir uma melhor descrição dos fenómenos de endurecimento cíclico. Para tal, foi considerado um modelo reológico modificado de endurecimento cinemático e usadas variáveis de estado adicionais. O desempenho dos modelos desenvolvidos na reprodução precisa de anisotropia plástica e fenómenos de endurecimento cíclico é avaliado através da sua implementação no código comercial Abaqus usando subrotinas de utilizador. A precisão e eficiência computacional dos modelos e algoritmos desenvolvidos são comparados entre si através de simulações de benchmarks. Estes benchmarks permitem a avaliação dos modelos na descrição de, por exemplo, defeitos na conformação de chapas metálicas, tais como a formação de orelhas e o retorno elástico, bem como a comparação da estabilidade e precisão dos algoritmos numéricos.

Thesis (Ph. D.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2006.
Mayne, Paul, Committee Chair ; Puzrin, Alexander, Committee Member ; Germanovich, Leonid, Committee Member ; Lowell, Robert, Committee Member ; Rix, Glenn, Committee Member.

Buried pipeline networks play a vital role in the transportation of oil and natural gas from centers of production to centers of consumption. A common manufacturing technique for such pipes is the UOE process, where a flat steel plate is first formed into a U shape, then into an O shape, welded at the seam, and mechanically expanded before being shipped on site. The UOE forming process deforms the pipe material plastically and induces residual strains in the pipe. Such pipes are commonly buried on side and then are pressurized under the high head of the fluids they convey which induce hoop stresses as high as 80% of the pipe yield strength. When buried pipelines cross the regions of discontinuous permafrost, they undergo differential frost heaving, inducing significant bending deformations, which potentially induce local buckling in the pipe wall. To control local buckling, design standards impose threshold limits on buckling strains. Such threshold values are primarily based on costly full-scale experimental results. Past nonlinear finite element analysis attempts aiming at determining the threshold buckling strains have neglected the presence of residual stresses induced by the UOE forming and were thus found to grossly overestimate the buckling strains compared to those based experiments. Within the above context, the present study focuses on developing a numerical technique to predict the residual stresses induced during UOE forming, and incorporating the induced residual stresses in 3D nonlinear FEA modeling to more reliably predict buckling strain limits. Comparisons with conventional analysis techniques that omit residual stresses reveal the importance of incorporating residual stresses induced in forming when quantifying buckling strains.

O objetivo precípuo deste estudo é a implementação computacional de modelos constitutivos elásticos e elastoplásticos para materiais com gradação funcional em regime de grandes deslocamentos e elevadas deformações. Para simular numericamente um problema estrutural, são empregados aqui elementos finitos sólidos (tetraédrico e hexaédrico) com ordem de aproximação polinomial qualquer. Grandezas da Mecânica Não Linear do Contínuo, como deformação e tensão, são utilizadas na formulação deste estudo. Para reproduzir os grandes deslocamentos, é empregada a análise não linear geométrica. A descrição adotada aqui é a Lagrangiana total, e o equilíbrio da estrutura é expresso pelo Princípio da Mínima Energia Potencial Total. Com relação à resposta elástica do material, são usadas leis constitutivas hiperelásticas, nas quais a relação tensão-deformação é obtida a partir de um potencial escalar. O comportamento elastoplástico do material é definido pela decomposição da deformação nas parcelas elástica e plástica, pelo critério de plastificação de von-Mises, pela lei de fluxo associativa, pelas condições de consistência e de complementaridade, pelo parâmetro de encruamento isotrópico e pelo tensor das tensões inversas, relacionado ao encruamento cinemático. Duas formulações elastoplásticas são utilizadas aqui: a de Green-Naghdi, na qual a deformação é decomposta de forma aditiva; e a hiperelastoplástica, em que o gradiente é decomposto de forma multiplicativa. É empregado também o conceito de material com gradação funcional (GF), a qual é definida como a variação gradual (contínua e suave) das propriedades constitutivas do material. A solução numérica do equilíbrio de forças é feita via método iterativo de Newton-Raphson. Para satisfazer o critério de plastificação, são utilizadas as estratégias de previsão elástica, e de correção plástica via algoritmos de retorno. Basicamente foram desenvolvidos cinco programas computacionais: o gerador automático das funções de forma; o gerador de malhas de elementos finitos sólidos; o código para análise de materiais em regime elástico; o código para análise de materiais em regime elastoplástico; e o programa de pós-processamento. Além desses, o aluno teve contato com os programas EPIM3D e DD3IMP ao longo de seu estágio de doutorado na Universidade de Coimbra (Portugal). Os programas EPIM3D e DD3IMP são empregados para analisar, respectivamente, materiais em regime elastoplástico, e processos de conformação de metais. Para o problema da barra sob tração uniaxial uniforme, são descritas equações e soluções analíticas para materiais homogêneos e com GF em regime elastoplástico. Para reduzir o tempo de simulação, foi empregada a programação em paralelo. De acordo com os resultados das simulações numéricas, as principais conclusões são: o refinamento da malha de elementos finitos melhora a precisão dos resultados para materiais em regimes elástico e elastoplástico; as formulações elastoplásticas de Green-Naghdi e hiperelastoplástica parecem ser equivalentes para pequenas deformações; a formulação hiperelastoplástica é equivalente ao modelo mecânico dos programas EPIM3D e DD3IMP para materiais em regime de pequenas deformações elásticas; foram constatados ganhos significativos, em termos de tempo de simulação, com a paralelização dos códigos computacionais de análise estrutural; e os programas desenvolvidos são capazes de simular - com precisão - problemas complexos, como a membrana de Cook e o cilindro fino transversalmente tracionado.
The main objective of this study is the computational implementation of elastic and elastoplastic constitutive models for functionally graded materials in large deformation regime. In order to numerically simulate a structural problem, the finite elements used are solids (tetrahedric and hexahedric) of any order of approximation. Entities from Nonlinear Continnum Mechanics, as strain and stress, are used in the present formulation. To reproduce the finite displacements, the geometrically nonlinear analysis is employed. The description adopted here is the total Lagrangian, and the structural equilibrium is expressed by means of the Principal of Minimum Total Potential Energy. Regarding the elastic material response, hyperelastic constitutive laws are used, in which the stress-strain relation is obtained from a scalar potential. The elastoplastic material behavior is defined by the strain decomposition in the elastic and plastic parts, by the von-Mises yield criterion, by the associative flow law, by the consistency and complementarity conditions, by the isotropic hardening parameter, and by the backstress tensor, related to the kinematic hardening. Two elastoplastic formulations are used here: the Green-Naghdi one, in which the strain is additively decomposed; and the hyperelastoplasticiy, in which the gradient is multiplicatively decomposed. The concept of functionally graded (FG) material, in which the constitutive properties vary gradually (continuous and smoothly), is also used. The numerical solution of the forces equilibrium is obtained via Newton-Raphson iterative procedure. In order to satisfy the yield criterion, the strategies of elastic prediction and plastic correction (via return algorithms) are used. Basically, five computer codes have been developed: the automatic shape functions generator; the solid mesh generator; the code for analysis of materials in the elastic regime; the code for analysis of materials in the elastoplastic regime; and the post-processor. Besides these, the student had contact with the programs EPIM3D and DD3IMP during his doctoral stage in the University of Coimbra (Portugal). The programs EPIM3D and DD3IMP are employed to analyze, respectively, materials in the elastoplastic regime, and sheet-metal forming processes. For the problem of the bar under uniform uniaxial tension, equations and analytical solutions are described for homogeneous and FG materials. To reduce the simulation time, the parallel programming has been employed. According to the numerical simulation results, the main conclusions are: the results accuracy is improved with mesh refinement for materials in the elastic and elastoplastic regimes; the Green-Naghdi elastoplastic formulation and the hyperelastoplasticity appear to be equivalent for small strains; the hyperelastoplastic formulation is equivalent to the mechanical model of the programs EPIM3D and DD3IMP for materials the small elastic strains regime; simulation time reduction has been obtained with the parallelization of the computer codes for structural analysis; the developed programs are capable of simulating, precisely, complex problems, such as the Cook\'s membrane and the pulled thin cylinder.

The implementation of the δ₀₊ᵣ model in a finite element program is discussed. The idea of considering damage as a structural performance helps to avoid singularity. Strategies in drift correction is considered. The generalized time finite element method (GTFEM) is also discussed and implemented. It shows improved accuracy and stability with highly non-linear material properties.

A relevant contribution in the explosion of the silicon photonics derives from its nonlinear optics branch, also called nonlinear silicon photonics. This research area exploits the tight confinement of the light, which is allowed by the high contrast index in the silicon sub-micron-structures, and the nonlinearity of silicon to produce (fabricate, develop) novel active devices on the chip scale. Despite of the plenty of third order nonlinear optical phenomena, silicon lacks the second order nonlinearity, which is an essential component of nonlinear optics. In fact, due to the inversion symmetry of its crystalline structure, silicon is characterized by a zero bulk second order nonlinear susceptibility in electric-dipole approximation. Hence, this thesis had the general goal to demonstrate the possibility to perform an all optical experiment of frequency conversion by making use of the second order nonlinear response induced in strained silicon waveguides. The necessary condition to have a bulk second order nonlinear response in silicon is the breaking of its centrosymmetry. This can be obtained by deforming the crystalline structure, for example, by means of a mechanical strain. Based on this approach, this thesis presents and discusses the results achieved in the characterization of the mechanical properties and the strain-induced second order nonlinearity of silicon-on-insulator (SOI) waveguides mechanically strained by using a stressing cladding layer deposited on the waveguide. In particular, the mechanical characterization has been performed by micro-Raman spectroscopy allowing to reconstruct for the first time the two dimensional spatial distribution of the strain across the waveguide cross-section and study its inhomogeneity by varying the stress applied by the cladding overlayer. The second order nonlinear response and the influence of the strain field on it have been experimentally investigated through Second Harmonic Generation (SHG) experiments in transmission configuration and theoretically analyzed, pointing out the strict dependence of the second order nonlinear susceptibility on the extent and inhomogeneity of the strain field.

A relevant contribution in the explosion of the silicon photonics derives from its nonlinear optics branch, also called nonlinear silicon photonics. This research area exploits the tight confinement of the light, which is allowed by the high contrast index in the silicon sub-micron-structures, and the nonlinearity of silicon to produce (fabricate, develop) novel active devices on the chip scale. Despite of the plenty of third order nonlinear optical phenomena, silicon lacks the second order nonlinearity, which is an essential component of nonlinear optics. In fact, due to the inversion symmetry of its crystalline structure, silicon is characterized by a zero bulk second order nonlinear susceptibility in electric-dipole approximation. Hence, this thesis had the general goal to demonstrate the possibility to perform an all optical experiment of frequency conversion by making use of the second order nonlinear response induced in strained silicon waveguides. The necessary condition to have a bulk second order nonlinear response in silicon is the breaking of its centrosymmetry. This can be obtained by deforming the crystalline structure, for example, by means of a mechanical strain. Based on this approach, this thesis presents and discusses the results achieved in the characterization of the mechanical properties and the strain-induced second order nonlinearity of silicon-on-insulator (SOI) waveguides mechanically strained by using a stressing cladding layer deposited on the waveguide. In particular, the mechanical characterization has been performed by micro-Raman spectroscopy allowing to reconstruct for the first time the two dimensional spatial distribution of the strain across the waveguide cross-section and study its inhomogeneity by varying the stress applied by the cladding overlayer. The second order nonlinear response and the influence of the strain field on it have been experimentally investigated through Second Harmonic Generation (SHG) experiments in transmission configuration and theoretically analyzed, pointing out the strict dependence of the second order nonlinear susceptibility on the extent and inhomogeneity of the strain field.

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.

Negli ultimi anni l'interesse generale nei dispositivi micro-elettro-meccanici e nano-elettro-meccanici (MEMS e NEMS) è aumentato esponenzialmente, soprattutto grazie all'ampia gamma di applicazioni in molteplici ambiti oltre quello ingegneristico. Lo studio di questi dispositivi e' principalmente guidato da i) l'esigenza pratica di supportatare la fabbricazione dei dispositivi e lo sviluppo evolutivo degli stessi con una modellazione affidabile, ii) l'interesse di scienziati e ricercatori nelle problematiche teorico-matematiche associate a dispositivi di micro e nano-scala. Si e' cosi' aperta una nuova finestra di studio su questioni fondamentali della meccanica ed in particolare nella statica e nella dinamica non lineare. Questa tesi vuole introdurre una modellazione innovativa per quanto riguarda la descrizione del comportamento statico e dinamico di microtravi per dispositivi risonanti. Dopo aver risposto al requisito fondamentale di attendibilita' della modellazione proposta, ulteriore attenzione e' posta alla facilita' di implementazione e non ultimo all'efficienza computazionale. L'approccio proposto in questo lavoro si basa su un modello elastico non classico (strain-gradient elasticity theory) e tiene conto dell'effetto di stretching nonlineare della trave deformata, nonche' di un carico assiale applicato. Un'attuazione elettrica include aspetti di multifisica nel modello ed introduce un'ulteriore fonte di nonlinearita' nelle equazioni: accurate correzioni tengono conto degli effetti di bordo derivanti dal campo elettrico. Dal momento che il comportamento meccanico è strettamente correlato ai fenomeni dissipativi, per comprendere appieno l'effetto dell'accoppiamento termoelastico, la descrizione e' arricchita con le espressioni descrittive dei fenomeni termici, ottenendo cosi' un sistema accoppiato di equazioni differenziali alle derivate parziali. Il modello unificato proposto e' capace di descrivere il comportamento termo-elastico sia attraverso una formulazione classica che con due distinte teorie generalizzate. Le equazioni sono manipolate mediante un metodo di approssimazione spettrale e successive simulazioni numeriche. Diverse analisi vengono effettuate per valutare l'influenza della modellazione non classica nella risposta della trave.
Over the last few years general interest in the linear and nonlinear static and dynamics of microelectromechanical and nanoelectromechanical systems (MEMS & NEMS) has increased exponentially. From one hand, there exists practical needs to support the fabrications with a reliable modeling; on the other hand, theoretical exciting problems arising from the behaviour observed in micro- and nano-scale mechanical devices has attracted scientists and researchers. This has opened up a new window into the study of fundamental questions in mechanics and in particular in nonlinear dynamics. This thesis wants to present new improvements in the MEMS modeling: the aim is to predict accurately the dynamical and the statical behaviour in microbeam resonators. The work has to address the mandatory request of reliability, also by taking a closer look on the implementation and the computational efficiency. The proposed approach permits to account for local properties at the microscale by using the strain-gradient elasticity theory, the effect of the nonlinear midplane stretching and of an applied axial load are considered as well. An electric-voltage difference, introducing into the model a further source of nonlinearity, is considered, including also a correction term for fringing-field-effects. Furthermore, since the mechanical behaviour is strictly correlated to the dissipation phenomena, to fully understand the thermoelastic coupling effects, we add the description of the thermal phenomena to the mechanical problem obtaining a system of two coupled PDEs. The governing equations, by making use of a unified model, are able to describe the response by using the classical thermoelastic formulation and two distinct generalized theories. The study is carried out by means of a spectral approximation method and numerical simulations. Several analysis are carried out to estimate the influence of the non classical modeling on the beam response.

The present work focuses on the formulation of a Continuum Damage Mechanics model for nonlinear analysis of masonry structural elements. The material is studied at the macro-level, i.e. it is modelled as a homogeneous orthotropic continuum. The orthotropic behaviour is simulated by means of an original methodology, which is based on nonlinear damage constitutive laws and on the concept of mapped tensors from the anisotropic real space to the isotropic fictitious one. It is based on establishing a one-to-one mapping relationship between the behaviour of an anisotropic real material and that of an isotropic fictitious one. Therefore, the problem is solved in the isotropic fictitious space and the results are transported to the real field. The application of this idea to strain-based Continuum Damage Models is rather innovative. The proposed theory is a generalization of classical theories and allows us to use the models and algorithms developed for isotropic materials. A first version of the model makes use of an isotropic scalar damage model. The adoption of such a simple constitutive model in the fictitious space, together with an appropriate definition of the mathematical transformation between the two spaces, provides a damage model for orthotropic materials able to reproduce the overall nonlinear behaviour, including stiffness degradation and strain-hardening/softening response. The relationship between the two spaces is expressed in terms of a transformation tensor which contains all the information concerning the real orthotropy of the material. A major advantage of this working strategy lies in the possibility of adjusting an arbitrary isotropic criterion to the particular behaviour of the orthotropic material. Moreover, orthotropic elastic and inelastic behaviours can be modelled in such a way that totally different mechanical responses can be predicted along the material axes. The aforementioned approach is then refined in order to account for different behaviours of masonry in tension and compression. The aim of studying a real material via an equivalent fictitious solid is achieved by means of the appropriate definitions of two transformation tensors related to tensile or compressive states, respectively. These important assumptions permit to consider two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the fictitious space makes use of two scalar variables, which monitor the local damage under tension and compression, respectively. Such a model, which is based on a stress tensor split into tensile and compressive contributions that allows the model to contemplate orthotropic induced damage, permits also to account for masonry unilateral effects. The orthotropic nature of the Tension-Compression Damage Model adopted in the fictitious space is demonstrated. This feature, both with the assumption of two distinct damage criteria for tension and compression, does not permit to term the fictitious space as “isotropic”. Therefore, the proposed formulation turns the original concept of “mapping the real space into an isotropic fictitious one” into the innovative and more general one of “mapping the real space into a favourable (or convenient) fictitious one”. Validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry. The model is fully formulated for the 2-dimensional case. However, it can be easily extended to the 3-dimensional case. It provides high algorithmic efficiency, a feature of primary importance when analyses of even large scale masonry structures are carried out. To account for this requisite it adopts a strain-driven formalism consistent with standard displacement-based finite element codes. The implementation in finite element programs is straightforward. Finally, a localized damage model for orthotropic materials is formulated. This is achieved by means of the implementation of a crack tracking algorithm, which forces the crack to develop along a single row of finite elements. Compared with the smeared cracking approach, such an approach shows a better capacity to predict realistic collapsing mechanisms. The resulting damage in the ultimate condition appears localized in individual cracks. Moreover, the results do not suffer from spurious mesh-size or mesh-bias dependence. The numerical tool is finally validated via a finite element analysis of an in-plane loaded masonry shear wall.

Spinal ligaments may be a significant source of chronic back pain, yet they are often disregarded by the clinical community due to a lack of information with regards to their material response, and innervation characteristics. The purpose of this dissertation was to characterize the material response of spinal ligaments and to review their innervation characteristics. Review of relevant literature revealed that all of the major spinal ligaments are innervated. They cause painful sensations when irritated and provide reflexive control of the deep spinal musculature. As such, including the neurologic implications of iatrogenic ligament damage in the evaluation of surgical procedures aimed at relieving back pain will likely result in more effective long-term solutions. The material response of spinal ligaments has not previously been fully quantified due to limitations associated with standard soft tissue testing techniques. The present work presents and validates a novel testing methodology capable of overcoming these limitations. In particular, the anisotropic, inhomogeneous material constitutive properties of the human supraspinous ligament are quantified and methods for determining the response of the other spinal ligaments are presented. In addition, a method for determining the anisotropic, inhomogeneous pre-strain distribution of the spinal ligaments is presented. The multi-axial pre-strain distributions of the human anterior longitudinal ligament, ligamentum flavum and supraspinous ligament were determined using this methodology. Results from this work clearly demonstrate that spinal ligaments are not uniaxial structures, and that finite element models which account for pre-strain and incorporate ligament’s complex material properties may provide increased fidelity to the in vivo condition.

Cells respond to their mechanical environment by changing shape and size, migrating, or even differentiating to a more specialized cell type. A better understanding of the response of cells to surrounding cues will allow for more targeted and effected designs for biomedical applications, such as disease treatment or cellular therapy. The spreading behavior of both human mesenchymal stem cells (hMSCs) and 3T3 fibroblasts is a function of substrate stiffness, and can be quantified to describe the most visible response to how a cell senses stiffness. The stiffness of the substrate material can be modulated by altering the substrate thickness, and this has been done with the commonly-used linearly elastic gel, polyacrylamide (PA). Though easy to produce and tune, PA gel does not exhibit strain-stiffening behavior, and thus is not as representative of biological tissue as fibrin or collagen gel. Fibroblasts on soft fibrin gel show spreading similar to much stiffer linear gels, indicating a difference in cell stiffness sensing on these two materials. We hypothesize cells can sense further into fibrin and collagen gels than linear materials due to the strain-stiffening material property. The goal of this work is to compare the material response of linear (PA) and strain-stiffening (fibrin, collagen gel) substrates through modulation of effective stiffness of the materials. The two-step approach is to first develop a finite element model to numerically simulate a cell contracting on substrates of different thicknesses, and then to validate the numerical model by quantifying fibroblast spreading on sloped fibrin and collagen gels. The finite element model shows that the effective stiffness of both linear and nonlinear materials sharply increases once the thickness is reduced below 10µm. Due to the strain-stiffening behavior, the nonlinear material experiences a more drastic increase in effective stiffness at these low thicknesses. Experimentally, the gradual response of cell area of HLF and 3T3 fibroblasts on fibrin and collagen gels is significantly different (p<0.05) from these cell types on PA gel. This gradual increase in area as substrate thickness decreases was not predicted by the finite element model. Therefore, cell spreading response to stiffness is not explained by just the nonlinearity of the material.

The main focus of this work lies in the simulation of the deformation of mechanical components which consist of nonlinear elastic, incompressible material and that are subject to large deformations. Starting from a nonlinear formulation one can derive a discrete problem by using linearisation techniques and an adaptive mixed finite element method. This turns out to be a saddle point problem that can be solved via a Bramble-Pasciak conjugate gradient method. With some modifications the simulation can be improved.

A novel observational method for studying internal features in the coastal ocean is devel- oped and tested in a study of large nonlinear internal solitary-like waves. Observations were carried out in the southern Strait of Georgia in the summers of 2001 and 2002. By quantitatively combining photogrammetrically rectified oblique photo images from a circling aircraft with water column data we track a number of internal wave packets for periods of up to one hour and obtain a more complete view of internal waves, including propagation, oblique interaction, and generation. First, the applicability of various weakly nonlinear theories in modeling propagation of these large waves is tested. Both two-layer and continuous linear, KdV (Korteweg-de Vries), and BO (Benjamin-Ono) models are applied with and without background shear currents. After background shear currents are included, it is found that a continuously stratified BO equation can be used to model propagation speeds within ob- servational error, and that this is not true for other theories. Second, four observed oblique wave-wave interactions including two Mach interactions, one interaction which varied from known interaction patterns, and one very shallow angle regular interaction are analyzed. An existing small-amplitude theory is applied but is found to overestimate the likelihood of Mach interaction at large amplitude. Finally, large-scale aerial surveys are mapped. Using speeds typical of observed waves, their time and place of origin are predicted. It is found that the observed waves are generated at the passes to the south of the Strait of Georgia and are released into the Strait after ebb tides.

Doutoramento em Engenharia Mecânica
The present work deals with the development of robust numerical tools for Isogeometric Analysis suitable for problems of solid mechanics in the nonlinear regime. To that end, a new solid-shell element, based on the Assumed Natural Strain method, is proposed for the analysis of thin shell-like structures. The formulation is extensively validated using a set of well-known benchmark problems available in the literature, in both linear and nonlinear (geometric and material) regimes. It is also proposed an alternative formulation which is focused on the alleviation of the volumetric locking pathology in linear elastic problems. In addition, an introductory study in the field of contact mechanics, in the context of Isogeometric Analysis, is also presented, with special focus on the implementation of a the Point-to-Segment algorithm. All the methodologies presented in the current work were implemented in a in-house code, together with several pre- and post-processing tools. In addition, user subroutines for the commercial software Abaqus were also implemented.
O presente trabalho foca-se no desenvolvimento de ferramentas numéricas robustas para problemas não-lineares de mecânica dos sólidos no contexto de Análises Isogeométricas. Com esse intuito, um novo elemento do tipo sólido-casca, baseado no método das Deformações Assumidas, é proposto para a análise de estruturas do tipo casca fina. A formulação proposta é validada recorrendo a um conjunto de problemas-tipo disponíveis na literatura, considerando tanto regimes lineares como não-lineares (geométrico e de material). É ainda apresentada uma formulação alternativa para aliviar o fenómeno de retenção volumétrica para problemas em regime linear elástico. Adicionalmente, é apresentado um estudo introdutório da mecânica Do conta to no contexto de Análises Isogeométricas, dando especial ênfase ao algoritmo de Ponto-para-Segmento. As metodologias apresentadas no presente trabalho foram implementadas num código totalmente desenvolvido durante o de correr do mesmo, juntamente com diversas ferramentas para pré- e pós processamento. Foram ainda implementadas rotinas do utilizador para o software comercial Abaqus.

In this work, ordered all-binary short-period strained InAs/GaAs superlattice quantum wells were studied as an alternative to strained ternary alloy InGaAs/GaAs quantum wells. InGaAs quantum wells QWs have been of great interest in recent years due to the great potential applications of these materials in future generations of electronic and optoelectronic devices. The all binary structures are expected to have all the advantages of their ternary counterparts, plus several additional benefits related to growth, to the elimination of alloy disorder scattering and to the presence of a higher average indium content.

A study on shape memory alloy materials as vibration dampers is reported. An important component is the strain rate-dependent and temperature-dependent constitutive behavior of shape memory alloy, which can significantly change its energy dissipation capacity under cyclic loading. The constitutive model used accounts for the thermo-mechanical strain rate-dependent behavior and phase transformation. With increasing structural flexibility, the hysteretic loop size of shape memory alloy dampers increases due to increasing strain rates, thus further decreasing the response of the structure to cyclic excitation. The structure examined is a beam, and its behavior with shape memory alloy dampers is compared to the same beam with conventional dampers. Parametric studies reveal the superior performance of the shape memory alloy over the conventional dampers even at the resonance frequency of the beam-damper system. An important behavior of the shape memory alloy dampers is discovered, in that they absorb energy from the fundamental and higher vibration modes. In contrast, the conventional dampers transfer energy to higher modes. For the same beam control, the stiffness requirement for the shape memory alloy dampers is significantly less than that of the conventional dampers. Response quantities of interest show improved performance of the shape memory alloy over the conventional dampers under varying excitation intensity, frequency, temperature, and strain rate.

Ce travail est centré sur l'étude des non-linéarités de deuxiéme ordre dans le silicium vers une modulation optique à faible puissance et haute vitesse. Étant un cristal centro-symétrique, le silicium ne possède pas une susceptibilité non linéaire de deuxiéme ordre (X2), ce qui inhibe l'effet Pockels, un effet électro-optique linéaire couramment utilisé dans la modulation de la lumière dans les communications optiques. Une solution possible pour vaincre cette limitation est par application de contraint et déformation de la maille cristalline, ce qui rompt localement la centro-symétrie du cristal et génère X2.Dans cette thèse, nous abordons le problème de la génération de X2 dans le silicium par l'utilisation de la contrainte, couvrant toutes les étapes de la recherche: nous partons de bases théoriques développées par nous, on simule l'ensemble des effets de contraints, optiques et électriques, on décrit la fabrication des dispositifs et finalement on présent la caractérisation expérimentale de ces dispositifs.Dans ce travail de recherche, nous avons pu détecter des effets très particuliers qui sont attribués au effet Pockels, comme par example une dépendance claire de l'orientation du cristal sur l'efficacité de la modulation et aussi la modulation à haute fréquences, plus élevées que celles attendues par autres contributions. Ces résultats sont très prometteurs et se composent d'une nouvelle étape vers la mise en œuvre, dans un avenir proche, de la modulation à grande vitesse et à faible puissance dans les dispositifs de silicium
This work is devoted to the study of second order nonlinearities in silicon towards low power, high speed modulation. Being a centro-symmetric crystal, silicon does not possess a second order nonlinear susceptibility (X2), which inhibits Pockels effect, a linear electro-optic effect commonly used in the modulation of light in high speed communications. A possible solution to overcome this limitation is by straining/deforming the crystal lattice, which locally breaks the centro-symmetry of the crystal and generates X2.In this thesis, we approach the problem of generating X2 in silicon through the use of strain, covering all the research stages: we depart from newly developed theoretical grounds, simulate together the strain, optical and electrical effects together, describe the fabrication of the devices and present the experimental characterization.In our research work, we were able to detect very particular effects which are attributed to Pockels effect, such as a clear dependence of the crystal orientation on the modulation efficiency and high speed modulation, at frequencies higher than those expected from other contributions. This results are very promising and consist on a step further towards the possible implementation of high speed, low power modulation in silicon devices in the near future

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are provided with a mixture of numerical techniques, which suggest strong mathematical consistency within the model for all theoretical assumptions made. A physical experiment was undertaken and the results prove to be inaccurate when using parameters derived from tensile tests, but when back calculating parameters from the beam test the model has a 14.40% error at its extreme against the experimental data suggesting the necessity for further testing.

Les structures à faibles ou moyennes épaisseurs sont naturellement présentes dans la plupart des installations de production d'énergie : bâtiment réacteur, tuyauteries sous pression, réservoirs métalliques ou bâches, cuve de réacteur, liners métalliques des enceintes de confinement pour ne citer que ceux‐là. Un besoin actuellement exprimé par les unités d'ingénierie d’EDF est la modélisation des phénomènes de cloquage de liners métalliques des bâtiments réacteur. Un liner est une structures de type tôle métallique assurant la fonction d’étanchéité des centrales nucléaires. Sa modélisation nécessite la prise en compte d’un phénomène de contact-frottement engendrant du pincement sur la coque, de la plasticité sous l’effet de cloquage et de la non linéarité géométrique (instabilité de type flambement). Pour modéliser le comportement thermomécanique d’une structure pareille, les éléments finis de plaques et coques actuellement disponible ne semblent pas être à la hauteur. Le premier verrou attribuable à ces éléments est l’hypothèse des contraintes planes qui empêche la prise en compte de certaines lois de comportement nativement tridimensionnelles. En deuxième lieu, du fait de leur formulation avec des degrés de liberté de rotations ces éléments n’offrent pas une facilité d’utilisation lorsqu’il s’agit de résoudre des problèmes prenant en compte les effets non-linéaires telles que les grande transformations géométriques, le contact-frottement bi-facial, le flambement et les pressions suiveuses. Une alternative serait d’utiliser des éléments volumiques standards. Cependant le coût de calcul prohibitif des ces derniers est difficilement accessible pour de nombreuses applications industrielles. Le but de ces travaux est de proposer une solution à cette problématique. Nous avons proposé une formulation élément fini de type solide-coque enrichie en pincement et capable de reproduire les comportements des structures minces avec une précision satisfaisante. Ce nouvel éléments fini fonctionnent avec tout type de loi de comportement tridimensionnelle sans restriction sur les champs de contraintes. On peut également l’utiliser pour tous les types de problèmes mécaniques : linéaire et non linéaire, contact frottement, grande transformation, flambement, pression suiveuse etc. Les simulations numériques réalisées montrent des performances satisfaisantes
Thin or medium-thick structures are naturally present in most power generation facilities: reactor building, pressurized pipelines, metal tanks or tarpaulins, reactor vessel, metal liners of containment chambers, to name but a few. A need currently expressed by EDF's engineering units is the modeling of the blistering phenomena of metal liners in reactor facilities. A liner is a metal sheet type structure that provides the impermeability function of nuclear power plants. Its modeling requires taking into account a contact-friction phenomenon causing pinching on the shell, plasticity under the effect of blistering and geometric nonlinearity (buckling type instability). To model the thermo-mechanical behavior of such a structure, the finite elements of plates and shells currently available do not seem to be up to the task. The first limitation attributable to these elements is the assumption of plane stresses which prevents the consideration of some natively three-dimensional constitutive laws. Secondly, due to their formulation with rotational degrees of freedom these elements do not offer facility of use when solving problems that take into account non-linear effects such as large geometric transformations, bi-facial friction-contact, buckling and following pressures. An alternative would be to use standard volume elements. However, the prohibitive computing cost of the latter is difficult to access for many industrial applications. The aim of this work is to propose a solution to this problem. We have proposed a solid-shell finite element formulation enriched in their pinching stress and strain and capable of reproducing accurately the behaviour of thin structures. This new finite element works with any type of three-dimensional behaviour law without restriction on stress fields. It can also be used for all types of mechanical problems: linear and nonlinear, frictional contact, large transformation, buckling, displacement-dependent pressure, etc. The numerical simulations carried out show satisfactory performances

This works presents a study about effective properties of porous solids with nonlinear elastic and elastoplastic matrix. For macroscopic mechanics properties evaluation, micromechanics models are used with effective strain concept relative to the modified second method. The porous are assumed as randomly distributed in the matrix, which presents a constitutive law with linear behavior in dilatation and nonlinear in shear. The results are compared with those provided by finite element methods program ABAQUS, assuming porous with spherical geometry for three dimensional solids. Numerical results from ABAQUS were obtained by an implementation of an external subroutine which incorporates at analysis the nonlinear constitutive law.
CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico
Este trabalho apresenta um estudo sobre as propriedades efetivas de sólidos porosos com matriz elástica não linear e elastoplástica. Na avaliação das propriedades mecânicas macroscópicas empregam-se modelos micromecânicos lineares em conjunto com o conceito de deformação efetiva correspondente ao método secante modificado. Os poros são admitidos como distribuídos randomicamente na matriz, a qual apresenta uma lei constitutiva caracterizada por um comportamento linear em dilatação e não linear em cisalhamento. Os resultados obtidos são confrontados com aqueles fornecidos pelo programa comercial de elementos finitos ABAQUS, admitindo-se que os poros exibem geometrias esféricas para sólidos tridimensionais. A geração dos resultados numéricos oriundos do programa ABAQUS foi viabilizada mediante a implementação de uma sub-rotina externa que incorpora a relação constitutiva não linear considerada nas análises.

При традиційному підході оболонка з підкріпленими отворами розглядається як конструкція, що складається із власне оболонки і підкріплювальних одновимірних тонких стержнів. Напружено-деформований стан (НДС) кожного з цих елементів визначається рівняннями відповідної прикладної теорії і має свої особливості. Тому при побудові теорії, яка описує НДС оболонок з підкріпленими отворами, виникають труднощі, пов’язані з необхідністю врахування сумісної роботи елементів різної мірності і задоволення умов контакту.

O objetivo deste trabalho é tratar da simulação do fenômeno de propagação de ondas em uma haste heterogênea elástico, composta por dois materiais distintos (um linear e um não-linear), cada um deles com a sua própria velocidade de propagação da onda. Na interface entre estes materiais existe uma descontinuidade, um choque estacionário, devido ao salto das propriedades físicas. Empregando uma abordagem na configuração de referência, um sistema não-linear hiperbólico de equações diferenciais parciais, cujas incógnitas são a velocidade e a deformação, descrevendo a resposta dinâmica da haste heterogénea. A solução analítica completa do problema de Riemann associado são apresentados e discutidos.
The objective of this work is the simulation of the wave propagation phenomenon in a heterogeneous elastic rod, composed by two distinct materials (a linear and a non-linear one), each of them with its own wave propagation speed. At the interface between these materials there is a discontinuity, a stationary shock, due to the jump of the physical properties. Employing a reference configuration approach, a nonlinear hyperbolic system of partial differential equations, whose unknowns are the velocity and the strain, describing the dynamical response of the heterogeneous rod. The complete analytical solution of the associated Riemann problem is presented and discussed.

Orientadores: Maria Cecilia Amorim Teixeira da Silva, Mario Conrado Cavichia
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
Made available in DSpace on 2018-08-27T11:54:46Z (GMT). No. of bitstreams: 1 Bandini_PedroAlexandreConde_M.pdf: 4052076 bytes, checksum: d472c46210a38be12152d6d9d5366659 (MD5) Previous issue date: 2015
Resumo: A fim de atender a requisitos de Estados Limites de Serviço, uma estrutura de concreto deve satisfazer critérios, dentre eles o controle de deslocamentos excessivos. As normas de projeto de estruturas de concreto estabelecem limites máximos para flechas em vigas que devem ser verificados em etapa de projeto. Portanto, métodos que estimem os deslocamentos em vigas de concreto armado de maneira satisfatória devem ser utilizados por engenheiros estruturais com o intuito de se projetar estruturas que atendam às condições de segurança e de serviço. No presente trabalho foram desenvolvidos e implementados os procedimentos numéricos FLECHA-0 e FLECHA-T que permitem analisar o comportamento de vigas de seção retangular, bi-apoiadas, de concreto armado submetidas à flexão simples. Os procedimentos consideraram a não-linearidade física para o cálculo de flecha imediata e flecha total, nesta sendo também considerados os efeitos de fluência e retração. Adotou-se a análise da seção transversal em camadas para integração das tensões e obtenção dos esforços internos. A consideração da não-linearidade física foi introduzida através do emprego de modelos constitutivos adequados para concreto e aço, e a colaboração do concreto entre fissuras foi considerada através de modelo de tension-stiffening para o concreto tracionado pós-fissuração em região de tração efetiva. A análise de efeitos diferidos de fluência e retração foi desenvolvida mediante emprego de método para cálculo de curvatura em elementos fletidos. Os procedimentos numéricos foram implementados computacionalmente e foram validados através da comparação com resultados experimentais de vigas ensaiadas à flexão obtidos por outros pesquisadores. Também foram avaliadas as recomendações referentes ao cálculo de flecha em vigas apresentadas pelas normas brasileira e europeia. Devido aos resultados obtidos na análise comparativa a modelos experimentais, procedeu-se uma investigação da influência da taxa de armadura de tração no procedimento para cálculo de flecha imediata em vigas recomendado pela norma brasileira de projeto de estruturas de concreto. Os resultados obtidos pelos procedimentos numéricos desenvolvidos no presente trabalho (FLECHA-0 e FLECHA-T) foram satisfatórios comparados aos experimentais e indicaram que estes podem ser empregados em situações de projeto para verificação de Estado Limite de Serviço de Deformações Excessivas em vigas de concreto armado do grupo I de resistência. A análise da influência da taxa de armadura de tração indicou que pode existir uma limitação ao uso do procedimento recomendado pela norma brasileira para o cálculo de flecha imediata em vigas com taxa de armadura inferior de tração a 0,50%
Abstract: In order to satisfy Serviceability Limits States requirements, a concrete structure must fulfill some criteria; among them is the deflection control. Guidelines for the design of concrete structures set maximum limit to the deflection of beams which ought to be verified at the design stage. Therefore, methods which are able to estimate deflection of reinforced concrete beams satisfactorily should be used by the structural designer in order to design a RC structure that meet safety and serviceability specifications. This work presents the development of numerical procedures called FLECHA-0 and FLECHA-T that allow the assessment of instaneous and long-term (considering creep and shrinkage effects) deflections, respectivly, on reinforced concrete simply supported rectangular beams subjected to bending. A section analysis approach was adopted for the integration of stresses to obtain bending moment and axial load acting on the section and material nonlinearities were introduced by the application of adequate constitutive relations for concrete and steel. The collaboration of concrete in tension between cracks was considered by a tension-stiffening model for post-cracking concrete under tension. The numerical procedures were implemented and their efficiencies were verified by the comparison to experimental results of tested RC beams under bending. Specifications related to the subject, established by the Brazilian and European standards guidelines were also investigated. Due to the results gathered in the comparative analysis to experimental data, an investigation was perfomed to assess the influence of the tension reinforcement ratio on the procedure to estimate instantaneous deflection in beam recommended by the Brazilian concrete structures design standards. The results obtained by the numerical procedures developed in the present work (FLECHA-0 and FLECHA-T) showed to be satisfactory and indicate that such procedures are able to be applied at design situations for the assessment of Deflection Control Serviceability Limit State in reinforced concrete beams of the strength group I. The analysis of the influence of the tension reinforcement ratio indicated that a limitation may exist in the procedure recommended by the Brazilian standards when applied to estimate instantaneous deflection of beams with tension reinforcement ratio lower than 0.50%
Mestrado
Estruturas e Geotécnica
Mestre em Engenharia Civil

ABSTRACT 3-D SOIL STRUCTURE INTERACTION ANALYSES OF THREE IDENTICAL BUILDINGS IN SAKARYA CITY AFTER 17 AUGUST 1999 KOCAELI EARTHQUAKE Ü
nal,Orhan M.S., Department of Civil Engineering, Supervisor: Assist. Prof. Dr Kemal Ö
nder Ç
etin October 2003, 116 Pages The aim of this study is to analyze the soil structure interaction of three identical buildings on ª
ahinler Street of Sakarya city which had no damage to heavy damage after the Kocaeli (1999) earthquake. For the purpose of 3-D dynamic nonlinear analysis of the soil site and the overlying structures, Flac3D software was chosen as the numerical modeling framework. Soil properties were determined by using the results of available site investigation studies. A three dimensional mesh was created to represent the topographic and geometric constraints of the problem. Linearly elastic perfectly plastic constitutive model was implemented to model the soil behavior. The results of 3-D dynamic numerical analyses in the forms of acceleration, displacement, strain, stress and pore pressure were presented. The higher acceleration, strain and stress levels calculated under the collapsed building can be attributed as the major cause of poor performance of the structure.

This thesis investigates the fatigue pull-through failures of steel roof batten to rafter connections and proposes suitable design equations to enhance the safety of thin steel roof battens in cyclones. Suitable design equations were developed based on both linear and nonlinear damage theories by carefully investigating the factors affecting the failure via small and full-scale experimental studies and associated numerical studies. The proposed design equations have the potential to replace the current Australian design method based on complex and time-consuming prototype cyclic tests, and also those used in many other countries.

Les tissus artériels sont constitués de réseaux de collagène et d'élastine diversement organisés et présentent un comportement anisotrope hautement non linéaire ainsi que la capacité de supporter de grandes déformations réversibles. Ces dernières s'accompagnent d'un réarrangement progressif des réseaux de fibres induit parle chargement. Dans cette thèse, l'important couplage entre la morphologie de la microstructure artérielle et sa réponse mécanique nous a motivé à développer un modèle multi-échelle détaillé de la paroi artérielle. Le cadre de la micromécanique des milieux continus a été utilisé dans une approche incrémentale pour calculer la contrainte, la déformation et les réorientations de fibres. Les extensions du problème d'inclusion de la matrice d'Eshelby permettent d'obtenir des expressions analytiques pour les tenseurs de concentration, qui relient le tenseur de vitesse de déformation macroscopique à la vitesse de déformation et à la vorticité moyennés sur les phases. Nous avons modélisé séparément le comportement de l'adventice et de la média, avant de proposer un modèle complet pour l'artère. De plus, le modèle de comportement multi-échelle a été implémenté dans une formulation éléments finis non linéaire, afin de réaliser des calculs de structure sur l'artère. Le modèle a été validé par différents ensembles de données expérimentales sur des échantillons artériels de différentes espèces. Les résultats montrent que le modèle est capable d'estimer la contribution de chaque tunique dans la réponse macroscopique du tissu pour différents chargements et peut prédire avec précision à la fois la réponse macroscopique et la cinématique microscopique des fibres
Arterial tissues are made of variously organized collagen and elastin networks and exhibit a highly nonlinear anisotropic behavior with the ability to sustain large reversible strains and to undergo a load-induced progressive morphological rearrangement of the microstructure. In the present study motivated by these specificities of arterial mechanics, we developed a detailed multi-scale model of the arterial wall. The framework of finite strain continuum micromechanics was employed in an incremental approach to compute stress, strain, and fiber reorientations. The extensions of Eshelby’s matrix-inclusion problem allowed for deriving analytical expressions for the concentration tensors, which relate the macroscopic strain rate tensor to phase-averaged strain rate and vorticity. The model accounts for the universal patterns across different scales in the two mechanically significant layers of arteries, namely the adventitia and the media. Furthermore, the multi-scale constitutive model was implemented in a non-linear finite element formulation to solve the structural model of the artery. The model was validated against different experimental data sets on arterial samples from different species. The results show that the model is able to estimate the contribution of each component into the macroscopic response of the tissue for different loading and can predict both the macroscopic response and microscopic fiber kinematics accurately. We submit that such model would help in predicting the evolution of the mechanical tissue response overtime during, for instance, remodeling and growth or damage

Les matériaux composites à matrice organique sont largement utilisés dans l'industrie des transports et notamment dans le domaine aéronautique. Pour permettre un dimensionnement optimal des structures, il est nécessaire d'étudier le comportement des matériaux CMO sur une large gamme de vitesses et de températures.L'objectif de cette thèse est de proposer un modèle de comportement et de rupture permettant de prédire la réponse des CMO sur une large gamme de vitesses de sollicitation et de températures. Les recherches se sont intéressées dans un premier temps à la caractérisation de la transition entre les régimes de comportement linéaire et non linéaire du matériau unidirectionnel T700GC/M21 (renforts de fibres de carbone, résine époxy), ainsi qu'à la dépendance de cette transition à la vitesse de sollicitation et à la température. Les travaux se sont ensuite focalisés sur l'étude expérimentale du régime de comportement non linéaire endommageable du T700GC/M21. Enfin, au terme de ces deux étapes, une version améliorée du modèle disponible à l'ONERA pour les composites stratifiés (OPFM) a été proposée, version intégrant un critère de transition linéaire/non linéaire de comportement, et une prise en compte de l'influence de la vitesse de sollicitation et de la température sur la réponse du matériau
Nowadays, organic matrix composite materials are widely used in the transportation industry, and particularly in the aeronautical industry. To provide an optimal dimensioning of the structures, it is necessary to study the mechanical behavior of OMC on a large range of strain rates and temperatures. The aim of this PhD thesis is to propose a behavior and a rupture model to predict the mechanical response of OMC for a large range of strain rates and temperatures. The research was initially focused on the characterization of the transition between the linear and nonlinear behavior of the material T700GC/M21, a carbon / epoxy unidirectional laminate as well as the strain rate and temperature dependencies of this transition. The work was then focused on the experimental study of the nonlinear damaged behavior of the T700GC/M21. Finally, completing these first two steps, an updated version of the behavior model available at ONERA (OPFM) was proposed which includes the transition between linear and nonlinear behavior and the influence of strain rate and temperature on the mechanical response of the material