Dissertations / Theses on the topic 'Continuum Elasticity'
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1
Segall, Darren Eric 1970. "Coarse-graining electronic behavior in condensed matter systems : from electrons to continuum elasticity." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29307.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.Includes bibliographical references (leaves 131-137).
In this thesis properties of various condensed matter systems are studied, whose dependency on electronic behavior is incorporated through coarse-grained interactions. Three specific systems are considered. In the first system of study, high momentum, plane wave states of the electronic wave function are coarse-grained, while the low momentum states are fully resolved. Moreover, the coarse-graining procedure incorporates the response of the high momentum states to environmental changes and its couplings to changes in the low momentum states. Within density functional theory this allows the representation of the electronic wave function, when using a plane wave basis, to be computationally feasible without having to make the pseudopotential approximation. This coarse-graining procedure is beneficial for the study of high pressure systems, where the response of the core region is important. With this method we study a number of solid phases of boron and reveal a number of important structural and electronic properties on its high pressure and superconducting phase. The second system of study focuses on a slightly coarser scale, where a theory for the elasticity of nanometer sized objects is developed. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and acts as a bridge between the atomic and the continuum regimes. This theory properly describes elastic fluctuations on length scales on the order of the decay length of the force constant matrix; allowing for straightforward development of new relations between the bending and stretching properties of nanomechanical resonators, which prove to be much more accurate than the continuum-based relations currently employed in experimental analysis.
(cont.) This theory is then used to link features of the underlining electronic structure to the local elastic response in silicon nanoresonators, emphasizing the importance of electronic structure on the local and overall elastic response. Our final system of study focuses on the longest length scales, the continuum. It is shown that the inclusion of electronic structure is crucial in the study of the role of dislocations on the macroscopic property of slip. This thesis explores the discrepancy between experimental data and theoretical calculations of the lattice resistance in bcc metals. This thesis presents results for the temperature dependence of the Peierls stress and the first ab initio calculation of the zero-temperature Peierls stress which employ periodic boundary conditions. The ab initio value for the Peierls stress is over five times larger than current extrapolations of experimental lattice resistance to zero-temperature. Although it is found that the common techniques for such extrapolation indeed tend to underestimate the zero-temperature limit, in this work it is shown that other mechanisms other than the simple Peierls mechanism are important in controlling the process of low temperature slip.
by Darren Eric Segall.
Ph.D.
2
CADELANO, EMILIANO. "Graphene under strain. A combined continuum-atomistic approach." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/265920.
Full textAbstract:
By combining continuum elasticity theory and atomistic simulations,
we provide a picture of the elastic behavior of graphene,
which was addressed as a two-dimensional crystal membrane.
Thus, the constitutive nonlinear stress-strain relations for graphene,
as well as its hydrogenated conformers, have been derived in
the framework of the two-dimensional elastic theory, and all the
corresponding linear and nonlinear elastic moduli have been computed
by atomistic simulations. Moreover, we discuss the effects
of an applied stretching on graphene lattice to its electronic band
structure, in particular regards the concept of strain-induced
band gap engineering. Finally, we focus on the emergence of a
stretching field induced on a graphene nanoribbon by bending,
providing that such an in-plane strain field can be decomposed
in a first contribution due to the actual bending of the sheet and
a second one due to the edge effects induced by the finite size of
the nanoribbon.------------------------------------------------------ABSTRACT ITA-------Combinando la teoria dell‘elasticità del continuo con calcoli
eseguiti attraverso simulazioni atomistiche, si è affrontato lo
studio del comportamento elastico del grafene, ovvero di una
struttura cristallina bidimensionale a base carbonio. In tal modo,
nell‘ambito della teoria elastica bidimensionale, sono state derivate
le equazioni costitutive non lineari per il grafene e per il suo composto
con l‘idrogeno, detto grafane; conseguentemente sono stati
determinati per mezzo di simulazioni atomistiche tutti i relativi
moduli elastici lineari e non lineari. Inoltre, abbiamo discusso gli
effetti dovuti a deformazioni omogenee applicate al reticolo di
grafene sulle sue bande elettroniche, con particolare attenzione
al concetto di ingegnerizzazione della gap elettronica indotta
da deformazione. Infine, discutiamo l‘insorgenza di un campo
di deformazione su un campione di grafene finito sottoposto a
piegamento, evidenziando come tale campo possa essere decomposto
in un contributo causato della flessione reale subita e in un
secondo dovuto ai soli effetti di bordo.
v
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Ayoub, Sherif Fathy. "Analysis of elastic-plastic continuum at large deformation using hybrid descriptions and finite element method /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487265555439612.
Full text
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SALVALAGLIO, MARCO. "Continuum modeling of vertical heterostructures: elastic properties and morphological evolution." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/100682.
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The development of cutting-edge opto- and micro-electronic devices requires novel fabrication techniques, able to deliver high-quality materials, monolithically integrable into Si-based technology. Theoretical models and simulations supporting the experimental activities are highly needed to fully understand the growth physics at the nano- and micro-scale and tailor semiconductor heterostructures for technological applications. In this work, the modeling of the plasticity onset and of the morphological evolution for Ge/Si vertical heterostructures is introduced, fostered by the peculiar features of such systems with respect to the standard heteroepitaxy. Indeed, the aim of this thesis is to understand the main properties of systems with large height-to-base aspect-ratios, in order to offer new solutions for the realization of heterostructures with unprecedented material quality. Continuum models are selected to describe length scales ranging from a few nanometers to microns, and time scales of minutes (or even more).
By means of the linear elasticity theory equations, solved by Finite Element Method (FEM) simulations, the competition between elastic and plastic relaxation in vertical Ge/Si systems is investigated. The critical parameters for the insertion of dislocations are determined for a single-layer structure, made of a SiGe layer on a Si pillar, and then generalized to multilayer configurations. Moreover, the possibility to achieve coherent structures at any size is demonstrated, provided that a proper grading of the Ge content during the growth is considered. A recipe for the calculation of such a grading of the Ge content is also introduced. Several comparisons with experiments show the generality of the proposed investigation for heterostructures at the nanoscale, and the versatility of the developed method. Moreover, thanks to dedicated experiments stimulated by the theoretical predictions, dislocation-free structures are proven to be feasible also at the micrometer scale.
The three-dimensional evolution in time of vertical microcrystals is investigated by means of a phase-field model and FEM simulations. In particular, the annealing of Ge on Si microcrystals is modeled by considering the surface diffusion driven by the tendency toward the minimization of the surface energy. This allows the evolution induced by annealing of single structures to be described. Moreover, the coalescence mechanism for crystal arrays, resulting in the formation of a suspended film, is predicted. Such an evolution is confirmed by dedicated experiments and leads to the fabrication of a promising system for the high-quality heterogeneous integration of semiconductors. The coalescence occurring for closely spaced crystals during high-temperature growth is also assessed. The original extensions of the PF model, required by the theoretical investigations of the morphological evolution, are illustrated in the details. Particular attention is devoted to the description of anisotropic surface energies responsible for crystal faceting in thermodynamic regimes. Moreover, further extensions of the method, dealing with an accurate description of the growth processes, are reported.
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Mühlich, Uwe. "Generalised continuum approach for modelling quasi-brittle failure." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-137217.
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A proper description of quasi-brittle failure within the frame of continuum Mechanics can only be achieved by models based on so-called generalised continua. This thesis focuses on a strain gradient generalised continuum and provides a specific methodology to derive corresponding models which account for the essential features of quasi-brittle failure. This methodology is discussed by means of four peer-reviewed journal articles. Furthermore, an extensive overview of the state of the art in the field of generalised continua is given at the beginning of the thesis. This overview discusses phenomenological extensions of standard Continuum Mechanics towards generalised continua together with corresponding homogenisation strategies for materials with periodic or random microstructureEine geeignete, kontinuumsmechanische Beschreibung quasi-spröden Versagens ist nur unter Verwendung verallgemeinerter Kontinuumstheorien möglich. In dieser Habilitationsschrift stehen sogenannte Gradientenkontinua im Vordergrund. Für diese wird eine Methodik vorgeschlagen, welche die Herleitung von Modellen erlaubt, die in der Lage sind, quasi-sprödes Versagen adäquat abzubilden. Diese Methodik wird anhand von vier Publikationen dargestellt und diskutiert. Ein umfangreicher Überblick über den Stand der Forschung auf dem Gebiet der veralgemeinerten Kontinuumstheorien wird am Anfang der Habilitationschrift gegeben. Dabei werden neben phänomenologischen Ansätzen zur Ableitung verallgemeinerter Kontinuumstheorien auch die entsprechenden Homogenisierungskonzepte dargestellt. Letztere werden für Materialien mit periodischer Mikrostruktur und für Materialien mit zufälliger Mikrostruktur diskutiert
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Ortigosa, Martinez Rogelio. "On a new variational and computational framework for polyconvex nonlinear continuum mechanics and convex multi-variable nonlinear electro-elasticity." Thesis, Swansea University, 2016. https://cronfa.swan.ac.uk/Record/cronfa34893.
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The world of smart materials has experienced a dramatic revolution in the last decades. Electro Active and Magneto Active Materials are some of the most iconic of these, among which, dielectric and magnetostrictive elastomers are becoming extremely popular due to their outstanding actuation capabilities, and in lesser degree, to their energy harvesting capabilities. A clear example illustrating these extraordinary capabilities has been reported in the experimental literature, which has shown unprecedented extreme electrically induced deformations for the most representative dielectric elastomer, namely the acrylic elastomer VHB 4910.This thesis is focused on the development of well-posed constitutive models for nonlinear electro-elasticity in scenarios characterised by extreme deformations and extreme electric fields. This fundamental objective represents the underlying ingredient for the novel variational and computational frameworks developed hereby in the context of electro-elasticity. Very remarkably, the similarity between the equations in both electro-elasticity and magneto-elasticity, enables the variational and computational frameworks developed to be extended to the latter scenario, characterised by magnetomechanical interactions. Despite the enormous interest of the experimental and computational scientific community, the definition of suitable constitutive models is still at its early stages for both electro and magneto active materials. In the more specic context of elasticity, considerable effort has been devoted to the denition of polyconvex energy functionals, which entail the most widely accepted constitutive restriction, namely the ellipticity or Legendre-Hadamard condition. This condition, strongly related to the material stability of the constitutive equations, ensures the well-posedness of the governing equations. An extension of the ellipticity condition to the context of nonlinear electro-elasticity and hence, magneto-elasticity, is proposed in this work, ensuring the well-posedness of the equations for the entire range of deformations and electric or magnetic fields. It is important to emphasise that in this work, the extension of the ellipticity condition to the field of electro-elasticity is exclusively based on material stability considerations. The energy functional encoding the constitutive response of the electro active material is defined according to a novel convex multi-variable representation in terms of an extended set of arguments which ensures material stability. The extended set of arguments, including those characterising the concept of polyconvexity in the more specic scenario of nonlinear elasticity, is further enriched with additional electromechanical entities. Unfortunately, proof of sequential weak lower semicontinuity of the proposed definition of multi-variable convexity is not provided in this work. This condition, and the additional requirement of appropriate coercivity conditions on the energy functional, would ensure the existence of minimisers. Nevertheless, although of extreme relevance and scientific interest, this topic is not in the scope of the thesis and could be the objective of further research.
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Dingreville, Remi. "Modeling and Characterization of the Elastic Behavior of Interfaces in Nanostructured Materials: From an Atomistic Description to a Continuum Approach." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19776.
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Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2008.Committee Chair: Jianmin Qu; Committee Member: David McDowell; Committee Member: Elisa Riedo; Committee Member: Min Zhou; Committee Member: Mo Li.
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Quignon-Tosoni, Justine. "Rhéologie des matériaux pâteux : vers un continuum des régimes solide et liquide. Application aux boues résiduaires." Thesis, Clermont-Ferrand 2, 2015. http://www.theses.fr/2015CLF22629/document.
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Dans un contexte d’augmentation constante des volumes de boues d’épuration à traiter, l’optimisation du traitement des boues est un enjeu primordial. Les étapes de traitement, et de transport mettent en jeu des écoulements qu’il est nécessaire de comprendre et de prédire afin, par exemple, de pour pouvoir estimer les pertes de charges en conduite ou bien pour dimensionner les installations de pompage. D’un point de vue physique, les boues peuvent être considérées comme une suspension de particules dans un gel suspendant. Ainsi, le comportement rhéologique des boues d’épuration présente des similitudes importantes avec les suspensions colloïdales et les gels polymériques. Ces trois types de matériaux, i.e. les boues d’épuration, les gels colloïdaux et les suspensions polymériques, présentent un comportement rhéologique complexe dépendant du temps et de la sollicitation imposée. Ils présentent un comportement dual, solide aux contraintes faibles, et liquide pour des contraintes élevées. La transition solide-liquide est généralement modélisée par la définition d’un seuil de contrainte ou de déformation, supposé séparer les régimes solide et liquide. Cependant, cette notion de seuil suppose une transition abrupte, et s’oppose aux observations expérimentales qui mettent en évidence une transition continue et progressive. L’étude de la littérature a permis de mettre en évidence une nécessité d’améliorer la compréhension et la modélisation du phénomène de transition solide-liquide. De plus, il est nécessaire d’unifier la description des régimes solide et liquide sous un même modèle, afin de mettre en lien une continuité mathématique avec le caractère continu et progressif du phénomène physique modélisé. Une analyse des résultats disponibles dans la littérature nous a permis de construire un modèle mathématique unique pour décrire le comportement solide et le comportement liquide des matériaux étudiés. Les hypothèses posées à partir de la littérature pour construire ce modèle ont ensuite été validées expérimentalement. Le modèle proposé est basé sur la décomposition de la complaisance du matériau en la somme d’une contribution solide et d’une contribution liquide, dépendant du temps, de la sollicitation appliquée et de l’histoire du matériau. Ce modèle permet une description commune des comportements solides et liquides du matériau, en tenant compte de l’existence d’une élasticité résiduelle y compris pour des contraintes élevées, et d’une dissipation visqueuse faible pour les contraintes faibles, conformément aux résultats expérimentaux. Ces travaux de thèse ont permis de mettre en évidence le fait que le mécanisme de transition solide-liquide était piloté non pas par la contrainte ou par la déformation, mais par la complaisance du matériau. De plus, ils ont permis d’ouvrir la voie à une nouvelle manière d’appréhender la thixotropie et la transition solide-liquide des matériaux pâteux. En effet, le comportement d’un matériau pâteux est piloté par deux paramètres : un module élastique plateau correspondant à un état totalement structuré, et une viscosité infinie correspondant à un état totalement déstructuré. Ces paramètres intrinsèques au matériau sont alors pondérés par des évolutions de la microstructure, menant à une compétition entre les effets élastiques et les effets visqueux. Ainsi, la différence entre un comportement de type loi de puissance et un comportement de type loi de puissance à seuil peut être expliquée simplement par l’apparition d’effets élastiques non négligeablesIn a context of constant increasing volumes of wastewater treatment sludge, optimizing the treatment of sludge appears to be crucial. Each step of treatment and transportation involves flows. It appears necessary to understand and predict these flows in order, for example, to estimate pressure drops in pipes or to size properly pumping facilities. In a physical point of view, sludge can be considered as a suspension of particles in a gel. Thus, its rheological behaviour presents significant similarities to that of colloidal suspensions of polymeric gels. These three types of materials, i.e. wastewater treatment sludge, colloidal suspensions and polymeric gels, present a complex rheological behaviour which depend on both time and the applied solicitation. They exhibit a dual behaviour, solid at low shear stresses, and liquid when the applied shear stress is high. The solid-liquid behaviour is generally modelled by defining a critical shear stress or a critical strain, supposed to be the limit between the solid and liquid regimes. Nevertheless, this concept implies an abrupt transition, unlike experimental observations showing a continuous and progressive transition. The study of the literature permitted to highlight the need to improve the understanding and modelling of the solid-liquid transition. Moreover, it appears necessary to unify the description of the solid and liquid regime in a unique model, in order to link a mathematical continuity with thecontinuous and progressive nature of the physical phenomenon to model. The study of the results available in the literature permited us to build a unique mathematical model to describe both the solid behaviour and the liquid behaviour of the studied materials. The assumptions made from the literature results have thus been experimentally validated. The proposed model is based on the decomposition of the compliance of the material in the sum of a solid contribution and a liquid contribution, depending on time, the applied solicitation and the story of the material. This model permits a unique description of solide and liquid regimes of the material, taking into account the existence of a residual elasticity at high shear stresses, and a viscous dissipation for low shear stresses, in accordance with experimental results. This work permitted to highlight the fact that the solid-liquid transition mecanism is controlled by the compliance of the material, and not the shear stress or the strain. Moreover, it opened the way to a new way of understanding the thixotropy and the solid-liquid transition of pasty materials. Thus, the behaviour of a pasty material is controlled by two parameters : a plateau elastic modulus corresponding to a totally structured state, and an infinite viscosity corresponding to a totally destructured state. These parameters intrinsic to the material are pondered by the evolutions of the microstructure, leading to a competition between elastic and viscous effects. Thus, the difference between the power law behaviour and the Herschel-Bulkley behaviour can be simply explained by the apparition of elastic effects that can’t be neglected
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Beauregard, Matthew Alan. "Nonlinear Dynamics of Elastic Filaments Conveying a Fluid and Numerical Applications to the Static Kirchhoff Equations." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194164.
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Two problems in the study of elastic filaments are considered.First, a reliable numerical algorithm is developed that candetermine the shape of a static elastic rod under a variety ofconditions. In this algorithm the governing equations are writtenentirely in terms of local coordinates and are discretized usingfinite differences. The algorithm has two significant advantages:firstly, it can be implemented for a wide variety of the boundaryconditions and, secondly, it enables the user to work with generalconstitutive relationships with only minor changes to thealgorithm. In the second problem a model is presented describingthe dynamics of an elastic tube conveying a fluid. First weanalyze instabilities that are present in a straight rod or tubeunder tension subject to increasing twist in the absence of afluid. As the twist is increased beyond a critical value, thefilament undergoes a twist-to-writhe bifurcation. A multiplescales expansion is used to derive nonlinear amplitude equationsto examine the dynamics of the elastic rod beyond the bifurcationthreshold. This problem is then reinvestigated for an elastic tubeconveying a fluid to study the effect of fluid flow on thetwist-to-writhe instability. A linear stability analysisdemonstrates that for an infinite rod the twist-to-writhethreshold is lowered by the presence of a fluid flow. Amplitudeequations are then derived from which the delay of bifurcation dueto finite tube length is determined. It is shown that the delayedbifurcation threshold depends delicately on the length of the tubeand that it can be either raised or lowered relative to thefluid-free case. The amplitude equations derived for the case of aconstant average fluid flux are compared to the case where theflux depends on the curvature. In this latter case it is shownthat inclusion of curvature results in small changes in some ofthe coefficients in the amplitude equations and has only a smalleffect on the post-bifurcation dynamics.
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Lloyd, Jeffrey T. "Microstructure-sensitive simulation of shock loading in metals." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51853.
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A constitutive model has been developed to model the shock response of single crystal aluminum from peak pressures ranging from 2-110 GPa. This model couples a description of higher-order thermoelasticity with a dislocation-based viscoplastic formulation, both of which are formulated for single crystals. The constitutive model has been implemented using two numerical methods: a plane wave method that tracks the propagating wave front; and an extended one-dimensional, finite-difference method that can be used to model spatio-temporal evolution of wave propagation in anisotropic materials. The constitutive model, as well as these numerical methods, are used to simulate shock wave propagation in single crystals, polycrystals, and pre-textured polycrystals. Model predictions are compared with extensive existing experimental data and are then used to quantify the influence of the initial material state on the subsequent shock response. A coarse-grained model is then proposed to capture orientation-dependent deformation heterogeneity, and is shown to replicate salient features predicted by direct finite-difference simulation of polycrystals in the weak shock regime. The work in this thesis establishes a general framework that can be used to quantify the influence of initial material state on subsequent shock behavior not only for aluminum single crystals, but for other face-centered cubic and lower symmetry crystalline metals as well.
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MARZIANI, ROBERTA. "Asymptotic analysis of nonlinear models for line defects in materials." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/10041.
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The thesis is devoted to the study of the elastic behavior of solid crystals in the presence of dislocation defects by a variational point of view. In the first part we consider a Geometrically nonlinear elastic model in the three-dimensional setting, that allows for large rotations. Adopting a core approach, which consists in regularizing the problem at scale epsilon>0 around the dislocation lines, we perform the asymptotic analysis of the regularized energy as epsilon tends to 0. We focus in particular on the leading order regime and prove that the energy rescaled by $eps^2|logeps|$ Gamma converges to the line-tension for a dislocation density derived by Conti, Garroni and Ortiz in a three-dimensional linear framework.
The analysis is performed under the assumption that the dislocations are well separated at intermediate scale, this in fact will allow to treat individually each dislocation by means of a suitable cell formula.
The nonlinear nature of the energy requires that in the characterization of the cell formula we take into account that the deformation gradient is close to a fixed rotation.
In the second part we obtain the same Gamma-limit but starting from a nonlinear elastic model with mixed growth, that is we consider an elastic energy which is substantially quadratic far from the dislocations and sub-quadratic in the core region. This can be seen as another way of regularising the problem and allow us to slightly relax the diluteness condition of the admissible dislocation density and improve the compactness result obtained in the previous case.
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BOIOLI, FRANCESCA. "Dislocation modelling in realistic Si-Ge nanostructures." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/40115.
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SiGe heterostructures have gained a lot of interests in view of developing devices integrated into the main-stream Silicon technology and also from a scientific point of view as a prototypical system to understand the properties of more complex systems, such as III-V semiconductors. Si-Ge epitaxial structures, as well as other mismatched heteroepitaxial materials, have a high potential to improve the state-of-the-art of Si devices, thanks to the fact that the strain modifies the band structures of this material class, opening new possibility of band-gap engineering.
Since the nineties, the development of devices having strained-SiGe layers as the active part occurred, in particular the heterojunction bipolar transistors, further developed to what is presently the fourth-generation of SiGe technology. Also the introduction of strained Si layers by using relaxed SiGe virtual substrates, is very important, for example, for the complementary metal–oxide–semiconductor (CMOS) technology.
In order to effectively exploit SiGe or strained-Si layers in any application, it is fundamental to growth high quality single crystalline materials, reducing as much as possible the defect density in the active volume and the surface corrugation, and to obtain the desired strain state in the epitaxial layers. However the possibility of using such heterostructures for any application, is hindered by the nucleation of dislocation, which is often an unavoidable strain-relief mechanisms. Dislocation formation affects both the final material quality and the relaxation degree of mismatched layers. These defects are often charged and act as non-radiative recombination centers and it is generally accepted that they are detrimental for opto-electronic devices based on Si-Ge semiconductors. In the past years, a lot of effort has been devoted reduce the defect density or to segregate dislocations in non-active regions. However, dislocation engineering, intended as the precise control of dislocation position, has always been a goal out of reach, because of the nucleation of such defects at unpredictable sites at the surface or at other heterogeneities. It is clear that predicting the extent of the plastic relaxation process and governing dislocation nucleation and positioning would be of the utmost importance.
Self-assembled nanoislands and nanowires, represent other novel heterostructures that can be exploited to obtain defect-free configurations with the desired strain state. Even in this case, very high stresses arise from the epitaxial integration of lattice mismatched materials and dislocation formation remains a competitive strain relief mechanism. Hence it is of fundamental importance to determine the coherency limits of such nanostructures and to elucidate the main strain relief mechanisms in the attempt to predict the final dislocation microstructure and strain state in heteroepitaxial systems.
The main goal of this work, is the understanding of the fundamental mechanisms of dislocation nucleation and propagation in Si-Ge nanostructures (i.e. films, nanoislands and nanowires) through dislocation modelling. Even if dislocation formation and motion relies on a sequence of discrete atomic displacements, such defects induce in a crystal a smooth deformation field in the entire structure. The elastic theory of dislocations provides a good description of such stress field and of the elastic energy, as produced by dislocations in bulk materials or in finite size solids with simple geometries. In order to assess the stresses and the energetics of plastically relaxed multifaceted structures, characterized by an high surface to volume ratio and typical length scale in the order of tens or hundreds of nanometers, linear elasticity theory numerically solved by finite element methods is the most suitable tool, since in this approximation the dislocation-surface interaction can be correctly taken into account. Moreover, the motion of dislocations in nanostructures can be handled by using three-dimensional dislocation dynamics simulations. This simulation technique, originally developed to study plasticity in bulk materials, has been demonstrated to give accurate results also for nanometric systems, and is the tool of choice to study the motion and interactions of a large density of dislocation in thin films or three-dimensional nanocrystals. Important properties determined by the atomistic nature of dislocations moving in a discrete lattice, can be included, both in the finite element calculations and in dislocation dynamics simulations, by adopting simple rules that take into account such atomistic features.
The first topic addressed in this work, is the investigation of plastic relaxation in SiGe epitaxial films aimed at governing dislocation nucleation and positioning. In particular, we show with the help of finite element calculations and dislocation dynamics simulations that a turning point to direct dislocation formation and propagation in predefined regions, is the introduction of preferential nucleation sites through substrate nanopatterning. Theoretical predictions indicating effective dislocation trapping along the features of trench- or pit-patterned substrates are discussed and compared with tailored experiments of SiGe deposition on nanopatterned substrate.
The second issue investigated here concerns self-assembled SiGe nanoislands. In these epitaxial nanostructures an intriguing mechanism of dislocation ordering is observed. In this work we reproduced such behavior by using a simple analytical model based on energetics considerations. Furthermore, the plastic relaxation onset for dislocation formation has been determined in epitaxial islands grown on pit-patterned substrates and nucleated in pits. The key factors influencing dislocation formation in such structures have been identified, opening new possibility to grow large defect-free islands on nanopattered substrates.
Finally, dislocation formation in core-shell nanowires has been considered. Elastic and plastic strain relaxaion has been investigated in such structures and a mechanism for dislocation nucleation and propagation in core-shell nanowires is presented. This allowed us to predict dislocation configurations that are more efficient in the strain relief process and the expected misfit dislocation pattern at the core-shell interface.
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da, Silva Soares Joao Filipe. "Constitutive modeling for biodegradable polymers for application in endovascular stents." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85939.
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Percutaneous transluminal balloon angioplasty followed by drug-eluting stent
implantation has been of great benefit in coronary applications, whereas in peripheral
applications, success rates remain low. Analysis of healing patterns in successful
deployments shows that six months after implantation the artery has reorganized itself to
accommodate the increase in caliber and there is no purpose for the stent to remain,
potentially provoking inflammation and foreign body reaction. Thus, a fully
biodegradable polymeric stent that fulfills the mission and steps away is of great benefit.
Biodegradable polymers have a widespread usage in the biomedical field, such as
sutures, scaffolds and implants. Degradation refers to bond scission process that breaks
polymeric chains down to oligomers and monomers. Extensive degradation leads to
erosion, which is the process of mass loss from the polymer bulk. The prevailing
mechanism of biodegradation of aliphatic polyesters (the main class of biodegradable
polymers used in biomedical applications) is random scission by passive hydrolysis and
results in molecular weight reduction and softening.
In order to understand the applicability and efficacy of biodegradable polymers, a
two pronged approach involving experiments and theory is necessary. A constitutive
model involving degradation and its impact on mechanical properties was developed
through an extension of a material which response depends on the history of the motion
and on a scalar parameter reflecting the local extent of degradation and depreciates the
mechanical properties. A rate equation describing the chain scission process confers
characteristics of stress relaxation, creep and hysteresis to the material, arising due to the entropy-producing nature of degradation and markedly different from their viscoelastic
counterparts.
Several initial and boundary value problems such as inflation and extension of
cylinders were solved and the impacts of the constitutive model analyzed. In vitro
degradation of poly(L-lactic acid) fibers under tensile load was performed and
degradation and reduction in mechanical properties was dependent on the mechanical
environment. Mechanical testing of degraded fibers allowed the proper choice of
constitutive model and its evolution. Analysis of real stent geometries was made possible
with the constitutive model integration into finite element setting and stent deformation
patterns in response to pressurization changed dramatically as degradation proceeded.
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Fritsch, Andreas. "Multiscale explanation of elasticity and strength of bone and bone replacement materials made of hydroxyapatite, glass-ceramics, or titanium : a continuum micromechanics approach=mehrskalige erklärung der elastizit ät und festigkeit von knochen und knochenersatzmaterialien aus hydroxyapatit, glas-keramik oder titanium: ein kontinuumsmikromechanischer ansatz." Paris Est, 2009. http://pastel.archives-ouvertes.fr/docs/00/50/13/47/PDF/These_Fritsch_anglais.pdf.
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Knochen ist ein hierarchisch aufgebautes Material, gekennzeichnet durch eine erstaunliche Variabilität und Diversität. Knochenersatz- oder Biomaterialien sind wichtige Komponenten für künstliche Organe und werden auch als Gerüste für Tissue Engineering eingesetzt. Das Ziel dieser Dissertation ist die Vorhersage der Festigkeit von Knochen und Knochenersatzmaterialien auf Grund ihrer Zusammensetzung und Mikrostruktur mittels Mehrskalenmodellen. Die theoretischen Entwicklungen werden durch umfangreiche Experimente an kortikalen Knochen sowie an Biomaterialien aus Hydroxyapatit, Glas-Keramik und Titanium untermauertBone is a hierarchically organized material, characterized by an astonishing variability and diversity. Bone replacement or biomaterials are critical components in artificial organs, and they are also used as scaffolds in tissue engineering. The aim of this thesis is the prediction of the strength of bone and bone replacement materials, from their composition and microstructure, by means of multiscale models. The theoretical developments are supported by comprehensive experiments on cortical bone and on biomaterials made of hydroxyapatite, glass-ceramic, and titanium
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Nakhaei, Mohsen. "Layer-specific multiscale mechanical modeling of arterial structures with evolving fiber configurations." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEM014.
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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 fibresArterial 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
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Araujo, Robyn Patrice. "Mathematical modelling of mechanical stresses and vascular collapse in solid tumours." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/37156/6/37156_Digitised_Thesis.pdf.
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Della, Corte Alessandro. "Lattice structures with pivoted beams : Homogenization and nonlinear elasticity results." Thesis, Toulon, 2017. http://www.theses.fr/2017TOUL0019/document.
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Cette thèse est consacrée à la modélisation des structures fibreuses avec des milieuxcontinus généralisés. Dans l’Introduction, l'état de l'art concernant les milieuxcontinus généralisée et applications aux structures fibreuses sont décrits et lesproblèmes ouverts pertinents sont mis en évidence. Dans le Chapitre 1 et 2, uneprocédure d'homogénéisation rigoureuse basée sur des arguments de Gammaconvergenceest appliquée à une structure en treillis et à un model de poutrediscrétisé. Dans le Chapitre 3, un traitement variationnel est utilisé pour formuler unapproche favorable du point de vue numérique. Dans le Chapitre 4 sont discutées lesrésultats expérimentaux concernant le comportement de la structure dans différentstypes de déformation. Cela à motivé les études effectuées dans le Chapitre 5, ou lesMéthodes directes de calcul des variations sont appliquées à poutres d’Euler engrandes déformationsThis thesis focuses on the mathematical modeling of fibrous structures having somepeculiar properties (high strength-to-weight ratio and very good toughness infracture), whose mechanical behavior escapes from standard Cauchy elasticity. Inparticular, it addresses cases in which the presence of a microstructure, consisting ofregularly spaced pivoted beams, entails effects that are well described by generalizedcontinuum models, i.e. models in which the deformation energy density depends notonly on the gradient of the placement but also on the second (and possibly higher)gradients of it. In the Introduction, the state of the art concerning generalizedcontinua and their applications for the description of fibrous structures is describedand some relevant open problems are highlighted. In Chapter 1 and 2 a rigoroushomogenization procedure based on Gamma-convergence arguments is performedfor a lattice (truss-like) structure and for a discrete 1D system (Hencky-type beammodel). In Chapter 3, a variational treatment is employed to formulate acomputationally convenient approach. In Chapter 4 some experimental resultsconcerning the behavior of the structure in various kinds of deformation arediscussed. This motivated the investigation performed in Chapter 5, in which DirectMethods of Calculus of Variations are applied to Euler beams in large deformationsunder distributed load
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Fayolle, Séverine. "Sur l'analyse numérique de raccords de poutres et de plaques." Paris 6, 1987. http://www.theses.fr/1987PA066005.
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Formulation mécanique, mathématique et numérique des problèmes de raccord de structures minces constituées d'assemblages de poutres ou de plaques avec deux types de charnières: rigides ou élastiques. Démonstration de l'existence et unicité d'une solution pour les problèmes continus, avec convergence de la solution élastique vers la rigide quand l'élasticité diminue. Approximation des solutions par une méthode conforme d'éléments finis.
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Fischer, Paul [Verfasser], and Paul [Akademischer Betreuer] Steinmann. "C1 Continuous Methods in Computational Gradient Elasticity / Paul Fischer. Betreuer: Paul Steinmann." Erlangen : Universitätsbibliothek der Universität Erlangen-Nürnberg, 2011. http://d-nb.info/1015783635/34.
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Olive, Marc. "Géométrie des espaces de tenseurs : une approche effective appliquée à la mécanique des milieux continus." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4745/document.
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Plusieurs lois de comportement mécaniques possèdent une formulation tensorielle, comme c'est le cas pour l'élasticité où intervient un espace de tenseurs d'ordre 4, noté Ela. La classification des matériaux élastiques passent par la nécessité de décrire l'espace des orbites ELA/SO(3). Plus généralement, on étudie la géométrie d'un espace de tenseurs sur $mathbb{R}^{3}$, via l'action du groupe O(3). Cette géométrie est caractérisée par ses classes d'isotropies, ou encore classes de symétries. Tout espace de tenseurs possède en effet un nombre fini de classes d'isotropies. Nous proposons alors une méthode originale et générale pour obtenir ces classes d'istropie. Nous avons ainsi pu obtenir pour la première fois les classes d'isotropie d'un espace de tenseurs d'ordre 8 intervenant en théorie de l'élasticité linéaire du second-gradient de la déformation.Pour une représentation réelle d'un groupe compact, l'algèbre des polynômes invariants sépare les orbites, d'où la recherche d'une famille génératrice minimale de cette algèbre. Pour cela, on exploitant le lien entre les espaces de tenseurs et les espaces de formes binaires. Nous avons ainsi repris et ré-interprété les approches effectives de cette théorie, développées par Gordan au 19ième siècle. Cette ré-interprétation nous a permis d'obtenir de nombreux résultats, dont une famille génératrice minimale d'invariants pour l'élasticité mais aussi pour la piézoélectricté. Nous avons pu retrouver d'une façon simple les séries de Gordan, ainsi que des relations plus récentes d'Abdesselam--Chipalkatti sur les transvectants de formes binairesTensorial formulation of mechanical constitutive equations is a very important matter in continuum mechanics. For instance, the space of elastic tensors is a subspace of 4th order tensors with a natural SO(3) group action. More generaly, we have to study the geometry of a tensor space defined on $mathbb{R}^{3}$, under O(3) group action.To describe such a geometry, we first have to exhibit its isotropy classes, also named symetry classes. Indeed, each tensor space possesses a finite number of isotropy classes. In this present work, we propose an original method to obtain isotropy classes of a given tensor space. As an illustration of this new method, we get for the first time the isotropy classes of a 8th order tensor space occuring in second strain-gradient elasticity theory. In the case of a real representation of a compact group, invariant algebra seperates the orbits. This observation motivates the purpose to find a finite generating set of polynomial invariants. For that purpose, we make use of the link between tensor spaces and spaces of binary forms, which belongs to the classical invariant theory. We thus have to deal with SL(2,$mathbb{C}$) group action. To obtain new results, we have reformulated and reinterpreted effective approaches of Gordan's algorithm, developped during XIXth century. We then obtain for the first time a minimal generating family of elasticity tensor space, and a generating family of piezoelectricity tensor space. Using linear algebra arguments, we were also able to get important relations of classical invariant theory, such as the Gordan's series and the Abdesselam--Chipalkatti's quadratic relations on transvectants
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Sanchioni, Stefano. "Teoria ed applicazioni della meccanica dei continui." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12322/.
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L'obiettivo di questo lavoro è quello di fornire una panoramica sulla meccanica dei mezzi continui, sia da un punto di vista teorico, sia illustrando alcune importanti applicazioni. Il primo passo consiste nel definire i due approcci con cui si possono studiare i mezzi in questione, ovvero la descrizione lagrangiana ed euleriana, per poi elencare tutte le proprietà relative alle grandezze per le quali si scrivono le equazioni di bilancio. Nei capitoli successivi, si entrerà nel dettaglio di alcune di queste (leggi di bilancio della massa, dell'impulso e del momento angolare) e si approfondirà il concetto di tensore di stress. L'ultima parte della tesi sarà dedicata a mostrare come tutto ciò può essere applicato ai mezzi continui elastici e ai fluidi viscosi, con un focus sul principio di Bernoulli.
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Leta, James V. "An Elastica Model that Describes the Buckling of Cross-sections of Nanotubes." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1312166451.
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Azem, Leila. "Analyse des liens entre un modèle d'endommagement et un modèle de fracture." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX006/document.
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Cette thèse est consacrée à la dérivation des modèles de fracture comme limite de modèles d'endommagement.L'étude est justifiée essentiellement à travers des simulations numériques.On s'intéresse à étudier un modèle d'endommagement initié par Allaire, Jouve et Vangoethem.Nous apportons des améliorations significatives à ce modèle justifiant la cohérence physique de cette approche.D'abord, on ajoute une contrainte sur l'épaisseur minimale de la zone endommagée, puis on ajoute la condition d'irréversibilité forte.Nous considérons en outre un modèle de fracture avec pénalisation de saut obtenu comme limite asymptotique d'un modèle d'endommagement.Nous justifions ce modèle par une étude numérique et asymptotique formelle unidimensionnelle.Ensuite, la généralisation dans le cas 2D est illustrée par des exemples numériquesThis thesis is devoted to the derivation of fracture models as limit damage models.The study is justified mainly through numerical simulations.We are interested in studying a damage model initiated by Allaire, Jouve and Vangoethem.We are making significant improvements to this model justifying the physical consistency of the approach.First, we add a constraint on the minimum thickness of the damaged area and then we add a condition of strong irreversibility.We see also a fracture model with jump penalization obtained as an asymptotic limit of a damage model.We justify this model by a one-dimensional formal asymptotic numerical study.Then, the generalization in the case 2D is illustrated by numerical examples
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Jaravel, Julien. "Caractérisation in-situ et simulation numérique de la croissance de cavités dans un élastomère sous décompression de gaz." Phd thesis, Chasseneuil-du-Poitou, Ecole nationale supérieure de mécanique et d'aérotechnique, 2012. http://tel.archives-ouvertes.fr/tel-00785129.
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Cette thèse a porté sur l'endommagement par cavitation des élastomères soumis à une décompression de gaz. Des études ont montré qu'à partir d'un niveau de chargement hydrostatique, des cavités se forment dans un élastomère. Des cavités peuvent aussi apparaître dans un élastomère saturé en gaz lorsque la pression est brusquement supprimée. Les critères développés dans un cadre purement mécanique ont été utilisés pour essayer de prédire le phénomène observé sous chargement de gaz. La première étape du travail a consisté à caractériser expérimentalement les conditions spatiales et temporelles d'apparition de l'endommagement. Une pression macroscopique de gaz ou une contrainte hydrostatique critique ne peuvent pas pleinement prédire tous les cas observés. La diffusion de gaz ajoute un aspect temporel non négligeable. Ces résultats justifient l'étude numérique diffuso-mécanique couplée à l'échelle de la cavité qui a été conduite en considérant une cavité au centre d'un échantillon hyperélastique incompressible soumis à un chargement mécanique et à une diffusion de gaz. Ce modèle de sphère creuse a permis d'observer la croissance stable de la cavité pendant un cycle complet de chargement en gaz, avec un gonflement pendant la décompression. Ce gonflement a été couplé à un critère en allongement critique de la cavité pour reproduire les courbes donnant l'instant de cavitation pour les différents essais expérimentaux réalisés. Le modèle construit au aussi permis de reproduire qualitativement et quantitativement l'effet des paramètres du cycle en gaz sur le temps d'apparition des cavités, ainsi que l'effet de l'épaisseur des échantillons, ce qui n'avait pas été fait auparavant.
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Chen, Xiao-Ting. "Effet du chauffage sur le comportement mécanique et poro-mécanique de matériaux cimentaires : propriétés hydrauliques et changements morphologiques." Phd thesis, Ecole Centrale de Lille, 2009. http://tel.archives-ouvertes.fr/tel-00577102.
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Cette thèse a permis d'évaluer l'effet des changements de morphologie d'un matériau cimentaire soumis à un traitement thermique jusqu'à T (≤ 400°C). Pour cela, nous avons caractérisé expérimentalement le comportement mécanique (en compression uniaxiale, compression hydrostatique avec ou sans déviateur), poro-mécanique (modules d'incompressibilité Kb, Ks et coefficient de Biot b) et hydraulique (perméabilité au gaz), d'un mortier modèle E/C=0,5 suite à un cycle de chauffage/refroidissement. Les essais mécaniques multiaxiaux sont couplés aux mesures de perméabilité, qui servent d'indicateur de la progression de la fissuration du matériau sous contrainte. Nous avons également mis au point un essai original, permettant de quantifier le volume de l'espace poreux interconnecté sous chargement hydrostatique Pc. La création de porosité occluse sous l'effet d'un accroissement du confinement est confirmée, et ainsi la diminution de la rigidité de la matrice solide Ks avec Pc après traitement thermique T>200°C. Nous avons également identifié un effet bouchon (aucun passage de gaz) lors d'un chargement couplé, thermique et en compression hydrostatique du mortier mais aussi de bétons industriels (CERIB et ANDRA). Afin d'analyser l'évolution des propriétés mécaniques et poro-élastiques après traitement thermique, un modèle prédictif thermo-élasto-plastique avec endommagement isotrope et une approche micro-mécanique descriptive, intégrant la présence de micro-fissures, y sont couplés
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Baumgarten, Lars. "Gesteinsmechanische Versuche und petrophysikalische Untersuchungen – Laborergebnisse und numerische Simulationen." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2016. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-202612.
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Dreiaxiale Druckprüfungen können als Einstufenversuche, als Mehrstufenversuche oder als Versuche mit kontinuierlichen Bruchzuständen ausgeführt werden. Bei der Anwendung der Mehrstufentechnik ergeben sich insbesondere Fragestellungen hinsichtlich der richtigen Wahl des Umschaltpunktes und des optimalen Verlaufs des Spannungspfades zwischen den einzelnen Versuchsstufen. Fraglich beim Versuch mit kontinuierlichen Bruchzuständen bleibt, ob im Versuchsverlauf tatsächlich Spannungszustände erfasst werden, welche die Höchstfestigkeit des untersuchten Materials repräsentieren. Die Dissertation greift diese Fragestellungen auf, ermöglicht den Einstieg in die beschriebene Thematik und schafft die Voraussetzungen, die zur Lösung der aufgeführten Problemstellungen notwendig sind. Auf der Grundlage einer umfangreichen Datenbasis gesteinsmechanischer und petrophysikalischer Kennwerte wurde ein numerisches Modell entwickelt, welches das Spannungs-Verformungs-, Festigkeits- und Bruchverhalten eines Sandsteins im direkten Zug- und im einaxialen Druckversuch sowie in dreiaxialen Druckprüfungen zufriedenstellend wiedergibt. Das Festigkeitsverhalten des entwickelten Modells wurde in Mehrstufentests mit unterschiedlichen Spannungspfaden analysiert und mit den entsprechenden Laborbefunden verglichen.
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Dilbag, Singh. "Some dynamical problems in micropolar elasticity." Phd thesis, 2008. http://tel.archives-ouvertes.fr/tel-00573425.
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In this thesis, we have investigated some interesting dynamical problems in microstructural continuum using Eringen's polar theory. These problems are pertaining to surface waves in a microstretch plate, Stoneley waves at an interface between two different microstretch half-spaces, surface waves in a micropolar cylindrical borehole filled with micropolar fluid, reflection and transmission of elastic waves at a liquid/solid half-space and reflection of elastic waves from a micropolar mixture porous half-space.
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Hassanpour, Soroosh. "Dynamics of Gyroelastic Continua." Thesis, 2014. http://hdl.handle.net/10012/8289.
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This work is concerned with the theoretical development of dynamic equations for gyroelastic systems which are dynamic systems with four basic types of continuous mechanical influences, i.e. inertia, elasticity, damping, and gyricity or stored angular momentum. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing two different theories of elasticity, i.e. the classical and micropolar theories of elasticity, the energy expressions and equations of motion for the undamped classical and micropolar gyroelastic continua are derived. Whereas the micropolar gyroelastic continuum model with extra coefficients and degrees of freedom is primarily developed to account for the asymmetric elasticity, it also proves itself to be more comprehensive in describing the actual gyroscopic system or structure.
The dynamic equations of the general three-dimensional gyroelastic continua are reduced to the case of a one-dimensional gyroelastic continua in the three-dimensional space, i.e. three-dimensional gyrobeams. Two different gyrobeam models are developed, one based on the classical beam torsion and bending theories and one based on the simplified micropolar beam torsion and bending theories. Finite element models corresponding to the classical and micropolar gyrobeams are built in MATLAB and used for numerical analysis.
The classical and micropolar gyrobeam models are analyzed and compared, against the earlier gyrobeam models developed by other authors and also against each other, through numerical examples. It is shown that there are significant differences between the developed unrestricted classical gyrobeam model and the previously derived zero-order restricted classical gyrobeam models. These differences are more pronounced in the shorter beams and for the transverse gyricity case. The results also indicate that the unrestricted classical and micropolar gyrobeam models behave very diversely in a wide range of micropolar elastic constants even where the classical and micropolar elasticity models coincide.
As a foundation for development of the above-mentioned theories, the correct approach for simplification of the micropolar elasticity to the classical elasticity, the simple torsion and bending theories for micropolar beams, and the correct approximation of infinitesimal rotations or microrotations are derived and presented.
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Mühlich, Uwe. "Generalised continuum approach for modelling quasi-brittle failure." Doctoral thesis, 2013. https://tubaf.qucosa.de/id/qucosa%3A22912.
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A proper description of quasi-brittle failure within the frame of continuum Mechanics can only be achieved by models based on so-called generalised continua. This thesis focuses on a strain gradient generalised continuum and provides a specific methodology
to derive corresponding models which account for the essential features of quasi-brittle failure. This methodology is discussed by means of four peer-reviewed journal articles.
Furthermore, an extensive overview of the state of the art in the field of generalised continua is given at the beginning of the thesis. This overview discusses phenomenological extensions of standard Continuum Mechanics towards generalised continua together with corresponding homogenisation strategies for materials with periodic or random microstructure.:1 Introduction 7
2 Generalised Continua - a journey 9
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Principal classes of generalised continua . . . . . . . . . . . . . . . . . 10
2.2.1 Polar field theories and their relatives . . . . . . . . . . . . . . 10
2.2.2 Non-local continua . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Generalised continua by explicit homogenisation . . . . . . . . . . . . 15
2.3.1 Random micro-structures . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Periodic micro-structures . . . . . . . . . . . . . . . . . . . . . 18
2.3.3 Generalised homogenisation based on polynomials . . . . . . 20
3 Modelling of quasi-brittle failure 25
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Discussion of main results . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Bibliography 29
4 Collection of articles reflecting the author’s contribution 35Eine geeignete, kontinuumsmechanische Beschreibung quasi-spröden Versagens ist nur unter Verwendung verallgemeinerter Kontinuumstheorien möglich. In dieser Habilitationsschrift stehen sogenannte Gradientenkontinua im Vordergrund. Für diese wird eine Methodik vorgeschlagen, welche die Herleitung von Modellen erlaubt, die in der Lage sind, quasi-sprödes Versagen adäquat abzubilden. Diese Methodik wird anhand von vier Publikationen dargestellt und diskutiert. Ein umfangreicher Überblick über den Stand der Forschung auf dem Gebiet der veralgemeinerten Kontinuumstheorien wird am Anfang der Habilitationschrift gegeben. Dabei werden neben phänomenologischen Ansätzen zur Ableitung verallgemeinerter Kontinuumstheorien auch die entsprechenden Homogenisierungskonzepte dargestellt. Letztere werden für Materialien mit periodischer Mikrostruktur und für Materialien mit zufälliger Mikrostruktur diskutiert.:1 Introduction 7 2 Generalised Continua - a journey 9 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Principal classes of generalised continua . . . . . . . . . . . . . . . . . 10 2.2.1 Polar field theories and their relatives . . . . . . . . . . . . . . 10 2.2.2 Non-local continua . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Generalised continua by explicit homogenisation . . . . . . . . . . . . 15 2.3.1 Random micro-structures . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Periodic micro-structures . . . . . . . . . . . . . . . . . . . . . 18 2.3.3 Generalised homogenisation based on polynomials . . . . . . 20 3 Modelling of quasi-brittle failure 25 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Discussion of main results . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Bibliography 29 4 Collection of articles reflecting the author’s contribution 35
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Marquardt, Oliver [Verfasser]. "Implementation and application of continuum elasticity theory and a k · p model to investigate optoelectronic properties of semiconductor nanostructures / von Oliver Marquardt." 2010. http://d-nb.info/1007087366/34.
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Nel, Willem Petrus. "Structural integrity assessment of a low pressure turbine with transverse cracking." Thesis, 2009. http://hdl.handle.net/10210/2175.
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M.Ing.This dissertation deals with the structural integrity analysis of a low pressure (LP) turbine with transverse cracking. Cracks are initiated in the centre ring keyway of the shaft by a fretting mechanism and propagate during barring operation. The cracks arrest during normal operation when they are still relatively shallow. The aim of the calculations is to predict the transition where cracks start propagating by high cycle fatigue during normal operation of the shaft. Most influencing factors, including continuum mechanics, mathematical modelling, material behaviour, service loads and industry experience, are studied in detail as a precursor to the case study. The calculated results show that the case study is an example where the application of fracture mechanics on the crack-free stress field leads to erroneous results. There is a significant redistribution of stress in the presence of the crack so that the actual stress ratio, as calculated from three dimensional cracked models, varies significantly compared to the crack-free model. Calculated results, together with carefully researched material properties, confirm the postulated crack growth during barring operation and predict limiting crack sizes where high cycle fatigue would ensue during normal operation. The case study concludes that the shaft has a significant remaining life and that it can be returned to service with periodic non-destructive examinations.
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chen, Wei-liang, and 陳韋良. "Elasticity Analysis of Continuous Breast Ultrasound Images." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/48182092552492662615.
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碩士國立中正大學
資訊工程研究所
91
Elastography is a recently developed technique of imaging the tissue elasticity. The tissue elasticity of a lesion is also a useful US diagnosis criterion. In general, elastograms are created by comparing ultrasound (US) radio-frequency (RF) waveforms obtained before and after a light compression of the tissue. However, in this paper, the elasticity analysis is applied directly in the B-mode US images without the complicated RF extraction system. At first, a segmentation method, called level set, is used to segment the tumor contours from the continuous US images. Three elasticity features, contour difference, area difference and shift distance, are proposed to compare the tumor contours of the uncompressed and compressed US images. A shape feature, solidity, is also used for comparison. In general, the elasticity analysis is applied for two US images with and without compression. In this paper, the elasticity analysis is applied for the continuous 2D US images which are obtained during the probe being pressed. From the experimental results, the continuous elasticity analysis is better than the conventional elasticity analysis using only two images. One hundred of cases including 60 benign cases and 40 malignant cases are used in the experiments. An support vector machine based on the proposed four features is used to diagnosis the tumors. The accuracy of SVM is 87.00% (87/100) and the ROC area index AZ is 0.9140.
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Singh, Eeshitw Kaushal. "A Numerical Implementation of an Artery Model Using Hybrid Fem." Thesis, 2016. http://etd.iisc.ernet.in/handle/2005/2875.
Full textAbstract:
The goal of this thesis is to develop a hybrid _nite element formulation to carry out stress analysis of arteries. To the best of our knowledge, a hybrid _nite element impel mentation of the Holzapfel-Ogden artery model has not been carried out before. Since arteries are thin `shell-type' structures, they are subjected to membrane, shear and volumetric locking in case when standard _nite elements are used. Since hybrid _nite elements are known to overcome these problems, we develop hybrid hexahedral element formulations (both lower and higher-order) for artery analysis. We demonstrate The better coarse mesh accuracy of hybrid elements, which are based on a two-_eld variational formulation, over conventional displacement based elements. Typically, wend that three or four extra levels of renement are required with conventional elements to achieve the ame accuracy as hybrid elements. The recently proposed Holzapfel-Ogden constitutive model for the artery and its implementation both within the conventional and hybrid _nite element frameworks is discussed. The numerical implementation is particularly challenging due to the presence of _bers which can only take tensile loads. The mathematically exact tangent stiness matrix that we have derived in this work is crucial in ensuring convergence of the numerical strategy.
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Auffray, N. "Comportement des matériaux cellulaires : élaboration, caractérisation etmodélisation prédictive des propriétés." Phd thesis, 2008. http://tel.archives-ouvertes.fr/tel-00360837.
Full textAbstract:
Cette thèse a porté sur l'étude d'une classe de matériaux cellulaires, les micro nids d'abeille, destinés à combiner des propriétés mécaniques et acoustiques afin d'être employés comme absorbants acoustiques dans les tuyères des turbomachines. Les bonnes qualités d'absorption acoustique prédites par les modèles théoriques ont tout d'abord été vérifiées expérimentalement. Le travail s'est ensuite porté sur la modélisation des propriétés élastiques de ces structures. Pour ce faire une approche par milieu équivalent a été retenue et, de manière à tenir compte des effets d'échelle présents dans la structure, un milieu de substitution du type " élasticité du second gradient " a été choisi. Pour cela une méthode de construction par homogénéisation des opérateurs de cette loi de comportement a était introduite. Devant l'absence de résultats concernant les classes d'anisotropie des opérateurs d'élasticité dusecond ordre, une étude détaillée de ce point a conduit à l'identification des matrices à implémenter dans un code éléments finis. Les opérateurs du second ordre construits par homogénéisation ont pu ensuite être comparés à leurs formes théoriques. Ceci nous a permis de montrer que vis-à-vis du comportement de matériaux nida les effets du second ordre sont, dans certain cas, d'un ordre de grandeur comparable à ceux de l'élasticité classique. Les méthodes mises en place pour l'étude théorique des symétries des opérateurs d'élasticité sont généralisables à toutes lois de comportement linéaire.
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Lübbe, Jannis Ralph Ulrich. "Cantilever properties and noise figures in high-resolution non-contact atomic force microscopy." Doctoral thesis, 2013. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2013040310741.
Full textAbstract:
Different methods for the determination of cantilever properties in non-contact atomic force microscopy (NC-AFM) are under investigation. A key aspect is the determination of the cantilever stiffness being essential for a quantitative NC-AFM data analysis including the extraction of the tip-surface interaction force and potential. Furthermore, a systematic analysis of the displacement noise in the cantilever oscillation detection is performed with a special focus on the thermally excited cantilever oscillation. The propagation from displacement noise to frequency shift noise is studied under consideration of the frequency response of the PLL demodulator.
The effective Q-factor of cantilevers depends on the internal damping of the cantilever as well as external influences like the ambient pressure and the quality of the cantilever fixation.
While the Q-factor has a strong dependence on the ambient pressure between vacuum and ambient pressure yielding a decrease by several orders of magnitude, the pressure dependence of the resonance frequency is smaller than 1% for the same pressure range.
On the other hand, the resonance frequency highly depends on the mass of the tip at the end of the cantilever making its reliable prediction from known cantilever dimensions difficult.
The cantilever stiffness is determined with a high-precision static measurement method and compared to dimensional and dynamic methods. Dimensional methods suffer from the uncertainty of the measured cantilever dimensions and require a precise knowledge its material properties. A dynamic method utilising the measurement of the thermally excited cantilever displacement noise to obtain cantilever properties allows to characterise unknown cantilevers but requires an elaborative measurement equipment for spectral displacement noise analysis.
Having the noise propagation in the NC-AFM system fully characterised, a proposed method allows for spring constant determination from the frequency shift noise at the output of the PLL demodulator with equipment already being available in most NC-AFM setups.
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Baumgarten, Lars. "Gesteinsmechanische Versuche und petrophysikalische Untersuchungen – Laborergebnisse und numerische Simulationen." Doctoral thesis, 2015. https://tubaf.qucosa.de/id/qucosa%3A23031.
Full textAbstract:
Dreiaxiale Druckprüfungen können als Einstufenversuche, als Mehrstufenversuche oder als Versuche mit kontinuierlichen Bruchzuständen ausgeführt werden. Bei der Anwendung der Mehrstufentechnik ergeben sich insbesondere Fragestellungen hinsichtlich der richtigen Wahl des Umschaltpunktes und des optimalen Verlaufs des Spannungspfades zwischen den einzelnen Versuchsstufen. Fraglich beim Versuch mit kontinuierlichen Bruchzuständen bleibt, ob im Versuchsverlauf tatsächlich Spannungszustände erfasst werden, welche die Höchstfestigkeit des untersuchten Materials repräsentieren. Die Dissertation greift diese Fragestellungen auf, ermöglicht den Einstieg in die beschriebene Thematik und schafft die Voraussetzungen, die zur Lösung der aufgeführten Problemstellungen notwendig sind. Auf der Grundlage einer umfangreichen Datenbasis gesteinsmechanischer und petrophysikalischer Kennwerte wurde ein numerisches Modell entwickelt, welches das Spannungs-Verformungs-, Festigkeits- und Bruchverhalten eines Sandsteins im direkten Zug- und im einaxialen Druckversuch sowie in dreiaxialen Druckprüfungen zufriedenstellend wiedergibt. Das Festigkeitsverhalten des entwickelten Modells wurde in Mehrstufentests mit unterschiedlichen Spannungspfaden analysiert und mit den entsprechenden Laborbefunden verglichen.