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Статті в журналах з теми "Continuum micromorphe de Cosserat"
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Forest, S. "Homogenization methods and mechanics of generalized continua - part 2." Theoretical and Applied Mechanics, no. 28-29 (2002): 113–44. http://dx.doi.org/10.2298/tam0229113f.
Повний текст джерелаАнотація:
The need for generalized continua arises in several areas of the mechanics of heterogeneous materials, especially in homogenization theory. A generalized homogeneous substitution medium is necessary at the global level when the structure made of a composite material is subjected to strong variations of the mean fields or when the intrinsic lengths of non-classical constituents are comparable to the wavelength of variation of the mean fields. In the present work, a systematic method based on polynomial expansions is used to replace a classical composite material by Cosserat and micromorphic equivalent ones. In a second part, a mixture of micromorphic constituents is homogenized using the multiscale asymptotic method. The resulting macroscopic medium is shown to be a Cauchy, Cosserat, microstrain or a full micromorphic continuum, depending on the hierarchy of the characteristic lengths of the problem. .
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STEFANOU, IOANNIS, and JEAN SULEM. "THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES." Journal of Multiscale Modelling 02, no. 03n04 (September 2010): 217–34. http://dx.doi.org/10.1142/s1756973710000424.
Повний текст джерелаАнотація:
The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.
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Trinh, Duy Khanh, and Samuel Forest. "Generalized continuum overall modelling of periodic composite structures." Vietnam Journal of Mechanics 33, no. 4 (December 12, 2011): 245–58. http://dx.doi.org/10.15625/0866-7136/33/4/258.
Повний текст джерелаАнотація:
Classical homogenization methods fail to reproduce the overall response of composite structures when macroscopic strain gradients become significant. Generalized continuum models like Cosserat, strain gradient and micromorphic media, can be used to enhance the overall description of heterogeneous materials when the hypothesis of scale separation is not fulfilled. We show in the present work how the higher order elasticity moduli can be identified from suitable loading conditions applied to the unit cell of a periodic composite. The obtained homogeneous substitution generalized continuum is used then to predict the response of a composite structure subjected to various loading conditions. Reference finite element computations are performed on the structure taking all the heterogeneities into account. The overall substitution medium is shown to provide improved predictions compared to standard homogenization. In particular the additional boundary conditions required by generalized continua makes it possible to better represent the clamping conditions on the real structure.
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Nejadsadeghi, Nima, and Anil Misra. "Extended granular micromechanics approach: a micromorphic theory of degree n." Mathematics and Mechanics of Solids 25, no. 2 (October 16, 2019): 407–29. http://dx.doi.org/10.1177/1081286519879479.
Повний текст джерелаАнотація:
For many problems in science and engineering, it is necessary to describe the collective behavior of a very large number of grains. Complexity inherent in granular materials, whether due the variability of grain interactions or grain-scale morphological factors, requires modeling approaches that are both representative and tractable. In these cases, continuum modeling remains the most feasible approach; however, for such models to be representative, they must properly account for the granular nature of the material. The granular micromechanics approach has been shown to offer a way forward for linking the grain-scale behavior to the collective behavior of millions and billions of grains while keeping within the continuum framework. In this paper, an extended granular micromechanics approach is developed that leads to a micromorphic theory of degree n. This extended form aims at capturing the detailed grain-scale kinematics in disordered (mechanically or morphologically) granular media. To this end, additional continuum kinematic measures are introduced and related to the grain-pair relative motions. The need for enriched descriptions is justified through experimental measurements as well as results from simulations using discrete models. Stresses conjugate to the kinematic measures are then defined and related, through equivalence of deformation energy density, to forces conjugate to the measures of grain-pair relative motions. The kinetic energy density description for a continuum material point is also correspondingly enriched, and a variational approach is used to derive the governing equations of motion. By specifying a particular choice for degree n, abridged models of degrees 2 and 1 are derived, which are shown to further simplify to micro-polar or Cosserat-type and second-gradient models of granular materials.
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Tordesillas, Antoinette, Jingyu Shi, and John F. Peters. "Isostaticity in Cosserat continuum." Granular Matter 14, no. 2 (March 16, 2012): 295–301. http://dx.doi.org/10.1007/s10035-012-0341-4.
Повний текст джерела
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Gomez, Juan, and Cemal Basaran. "Computational implementation of Cosserat continuum." International Journal of Materials and Product Technology 34, no. 1/2 (2009): 3. http://dx.doi.org/10.1504/ijmpt.2009.022401.
Повний текст джерела
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Tang, Hong Xiang, and Chun Hong Song. "Finite Element Analysis of Strain Localization under Static and Dynamic Loading Conditions Based on Cosserat Continuum Model." Advanced Materials Research 250-253 (May 2011): 2510–14. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2510.
Повний текст джерелаАнотація:
In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the strain localization phenomena under static and dynamic loading conditions. The numerical studies on progressive failure phenomena, which occur in a panel, characterized by strain localization due to strain softening and its development, are numerically modelled by two types of Cosserat continuum finite elements, i.e. u8ω8 and u8ω4 elements. It is indicated that both two Cosserat continuum finite elements possess better performance in simulation of strain localization. Because of the presence of an internal length scale in Cosserat continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localization zone is computed under static as well as under transient loading conditions.
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Lalin, Vladimir, and Elizaveta Zdanchuk. "The Initial Boundary-Value Problem for a Mathematical Model for Granular Medium." Applied Mechanics and Materials 725-726 (January 2015): 863–68. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.863.
Повний текст джерелаАнотація:
In this work we consider a mathematical model for granular medium. Here we claim that Reduced Cosserat continuum is a suitable model to describe granular materials. Reduced Cosserat Continuum is an elastic medium, where all translations and rotations are independent. Moreover a force stress tensor is asymmetric and a couple stress tensor is equal to zero. Here we establish the variational (weak) form of an initial boundary-value problem for the reduced Cosserat continuum. We calculate the variation of corresponding Hamiltonian to obtain motion differential equation.
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Popov, V. L. "Coupling of an elastoplastic continuum and a Cosserat continuum." Russian Physics Journal 37, no. 4 (April 1994): 337–42. http://dx.doi.org/10.1007/bf00560216.
Повний текст джерела
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Tang, Hong Xiang, and Yu Hui Guan. "Finite Element Analysis of Stress Concentration Problems Based on Cosserat Continuum Model." Applied Mechanics and Materials 99-100 (September 2011): 939–43. http://dx.doi.org/10.4028/www.scientific.net/amm.99-100.939.
Повний текст джерелаАнотація:
In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the stress concentration problems. The stress concentration phenomena around circular hole, elliptic hole and rhombic hole in plane strain condition, are numerically simulated by two types of Cosserat continuum finite elements of the standard displacement and rotation u4ω4 and u8ω8 based on Dirichlet principle. It is indicated that, compared with the classical continuum finite element, these two Cosserat continuum finite elements can reflect the steep strain gradient and scale effects occurring in the stress concentration problems, and they can weaken the stress concentration and may get consistent solution with actual situation.
Дисертації з теми "Continuum micromorphe de Cosserat"
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Stathas, Alexandros. "Numerical modeling of earthquake faults." Thesis, Ecole centrale de Nantes, 2021. http://www.theses.fr/2021ECDN0053.
Повний текст джерелаАнотація:
Lors d’un glissement sismique, l’énergie libérée par la décharge élastique des blocs de terre adjacente peut être séparée en trois parties principales : L’énergie qui est rayonnée à la surface de la terre (_ 5% du budget énergétique total), l’énergie de fracture pour la création de nouvelles surfaces de faille et enfin, l’énergie dissipée à l’intérieur d’une région de la faille, d’épaisseur finie, que l’on appelle le “fault gouge ". Cette région accumule la majorité du glissement sismique. Estimer correctement la largeur de fault gouge est d’une importance capitale pour calculer l’énergie dissipée pendant le séisme, le comportement frictionnel de la faille et les conditions de nucléation de la faille sous la forme d’un glissement sismique ou asismique.Dans cette thèse, approches différentes de régularisation ont été explorées pour l’estimation de la largeur de localisation de la zone de glissement principal de la faille pendant le glissement cosmique. Celles-ci comprennent l’application de la viscosité et des couplages multiphasiques dans le continuum classique de Cauchy, et l’introduction d’un continuum micromorphe de Cosserat du premier ordre. Tout d’abord, nous nous concentrons sur le rôle de la régularisation visqueuse dans le contexte des analyses dynamiques, en tant que méthode de régularisation de la localisation des déformations. Nous étudions le cas dynamique d’un continuum de Cauchy classique adoucissant à la déformation et durcissant à la vitesse de déformation. En appliquant l’analyse de stabilité de Lyapunov, nous montrons que l’introduction de la viscosité est incapable d’empêcher la localisation de la déformation sur un plan mathématique et la dépendance de du maillage des éléments finis.Nous effectuons des analyses non linéaires en utilisant le continuum de Cosserat dans le cas de grands déplacements par glissement sismique de fault gouge par rapport à sa largeur. Le continuum de Cosserat nous permet de rendre compte de l’énergie dissipée pendant un séisme et du rôle de la microstructure dans l’évolution de la friction de la faille. Nous nous concentrons sur l’influence de la vitesse de glissement sismique sur le mécanisme d’assidument frictionnel de la pressurisation thermique. Nous remarquons que l’influence des conditions aux limites dans la diffusion du fluide interstitiel à l’intérieur de fault gouge, conduit à une reprise du frottement après l’affaiblissement initial. De plus, un mode de localisation de déformation en mouvement est présent pendant le cisaillement de la couche, introduisant des oscillations dans la réponse du frottement. Ces oscillations augmentent le contenu spectral du séisme. L’introduction de la viscosité dans le mode ci-dessus, conduit à un comportement de "rate and state" sans l’introduction d’une variable interne. Nos conclusions sur le rôle de la pressurisation thermique pendant le cisaillement de fault gouge sont en accord qualitatif avec les nouveaux résultats expérimentaux disponibles. Enfin, sur la base des résultats numériques, nous étudions les hypothèses du modèle actuel de glissement sur un plan mathématique proposent à la littérature. Le rôle des conditions aux limites et du mode de localisation des déformations dans l’évolution du frottement de la faille pendant le glissement sismique. Le cas d’un domaine délimité et d’un mode de localisation de la déformation en mouvement est examiné dans le contexte d’un glissement sur un plan mathématique sous pressurisation thermique. Nos résultats étoffent le modèle original dans un contexte plus généralDuring coseismic slip, the energy released by the elastic unloading of the adjacent earth blocks can be separated in three main parts: The energy that is radiated to the earth’s surface (_ 5% of the whole energy budget), the fracture energy for the creation of new fault surfaces and finally, the energy dissipated inside a region of the fault, with finite thickness, which is called the fault gauge. This region accumulates the majority of the seismic slip. Estimating correctly the width of the fault gauge is of paramount importance in calculating the energy dissipated during the earthquake, the fault’s frictional response, and the conditions for nucleation of the fault in the form of seismic or aseismic slip.In this thesis different regularization approaches were explored for the estimation of the localization width of the fault’s principal slip zone during coseismic slip. These include the application of viscosity and multiphysical couplings in the classical Cauchy continuum, and the introduction of a first order micromorphic Cosserat continuum. First, we focus on the role of viscous regularization in the context of dynamical analyses, as a method for regularizing strain localization. We study the dynamic case for a strain softening strain-rate hardening classical Cauchy continuum, and by applying the Lyapunov stability analysis we show that introduction of viscosity is unable to prevent strain localization on a mathematical plane and mesh dependence.We perform fully non linear analyses using the Cosserat continuum under large seismic slip displacements of the fault gouge in comparison to its width. Cosserat continuum provides us with a proper account of the energy dissipated during an earthquake and the role of the microstructure in the evolution of the fault’s friction. We focus on the influence of the seismic slip velocity to the weakening mechanism of thermal pressurization. We notice that the influence of the boundary conditions in the diffusion of the pore fluid inside the fault gouge, leads to frictional strength regain after initial weakening. Furthermore, a traveling strain localization mode is present during shearing of the layer introducing oscillations in the frictional response. Such oscillations increase the spectral content of the earthquake. Introduction of viscosity in the above mode, leads to a rate and state behavior without the introduction of a specific internal state variable. Our conclusions about the role of thermal pressurization during shearing of the fault gouge, agree qualitatively with newly available experimental results.Finally, based on the numerical findings we investigate the assumptions of the current model of a slip on a mathematical plane, in particular the role of the boundary conditions and strain localization mode in the evolution of the fault’s friction during coseismic slip. The case of a bounded domain and a traveling strain localization mode are examined in the context of slip on a mathematical plane under thermal pressurization. Our results expand the original model in a more general context
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ALAMO, FREDY JONEL CORAL. "DYNAMICS OF SLENDER ONE-DIMENSIONAL STRUCTURES USING COSSERAT CONTINUUM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9631@1.
Повний текст джерелаАнотація:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
Neste trabalho é formulado e analisado o equilíbrio estático e a dinâmica de uma viga elástica tridimensional. A teoria tridimensional empregada, que pode ser chamada de teoria de Cosserat para vigas, é exata geometricamente, ou seja, não está baseada em aproximações geométricas ou suposições mecânicas. Para a deformação da viga, assume-se a hipótese de Bernoulli e por simplicidade consideram-se relações constitutivas lineares para o material. A configuração deformada da viga é descrita através do vetor de deslocamento da curva de centróides, e uma base móvel, rigidamente unido à secção transversal da viga. A orientação da base móvel, relativo a um sistema inercial, é parametrizada usando três rotações elementares consecutivas. Na teoria de Cosserat para vigas, as equações do movimento são equações diferenciais parciais não-lineares em função do tempo e uma variável espacial. No entanto, para o equilíbrio estático, as equações tornam- se equações diferenciais ordinárias não-lineares com uma variável espacial que são resolvidas usando o método de perturbação. Da solução do equilíbrio estático, obtêm-se as funções de deslocamento da viga, em função dos deslocamentos e rotações nodais, as quais são usadas para a análise dinâmica. Para obter a dinâmica da viga usa-se a equação de Lagrange, que é formada pelas expressões da energia cinética e da energia potencial de deformação. Além disso, usa-se o método de Newmark para resolver as equações do movimento. Como aplicação, estuda-se numérica e experimentalmente, a dinâmica de uma viga rotativa curva contida numa cavidade uniforme. Quando se usa a teoria de Cosserat para vigas, que leva em conta as não linearidades geométricas, a alta precisão da resposta dinâmica é obtida dividindo o sistema em poucos elementos, as quais são bem menores que o tradicional MEF, essa é a principal vantagem da teoria desenvolvida.
In this work, it is formulated and analyzed the static equilibrium and the dynamics for three dimensional deformation of elastic rods. The intrinsically one-dimensional theory that is employed, which may be called the special Cosserat theory of rods, is geometrically exact, namely, it is not based upon geometrical approximations or mechanical assumptions. For the rod deformation, it is adopted the Bernoulli hypotheses and for simplicity, the linear constitutive relations are employed. The deformed configuration of the rod is described by the displacement vector of the deformed centroid curve and an orthonormal moving frame, rigidly attached to the cross-section of the rod. The orientation of the moving frame, relative to the inertial one, is related by the rotation matrix, parameterized by three elemental rotations. In the sense of Cosserat theory, the equations of motion are nonlinear partial dfferential equations, which are functions of time and one space variable. For the static equilibrium, however, the equations become nonlinear ordinary differential equations with one space variable, which can be solved approximately using standard techniques like the perturbation method. After the static equilibrium equation are solved, the displacement functions are obtained. These nonlinear displacement functions, which are functions of generic nodal displacements and rotations, are used for dynamical analysis. To obtain the dynamics of the Cosserat rod, it is used the Lagrangian approach, formed from the kinetic and strain energy expressions. Furthermore, the equations of motion, which are nonlinear ordinary dfferential equations, are solved numerically using the Newmark method. As an application, a curved rod, constrained to rotate inside a hole, is investigated numerically and experimentally. When using the Cosserat rod approach, that take into account all the geometric nonlinearities in the rod, the higher accuracy of the dynamic responses is achieved by dividing the system into a few elements, which is much less than in the traditional FEM
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Zaccaria, Federico. "Geometrico-static modelling of continuum parallel robots." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
Знайти повний текст джерелаАнотація:
In this thesis, we explore three methods for the geometrico-static modelling of
continuum parallel robots. Inspired by biological trunks, tentacles and snakes, continuum robot designs can reach confined spaces, manipulate objects in complex
environments and conform to curvilinear paths in space. In addition, parallel continuum manipulators have the potential to inherit some of the compactness and
compliance of continuum robots while retaining some of the precision, stability and
strength of rigid-links parallel robots.
Subsequently, the foundation of our work is performed on slender beam by applying the Cosserat rod theory, appropriate to model continuum robots.
After that, three different approaches are developed on a case study of a planar
parallel continuum robot constituted of two connected flexible links. We solve the
forward and inverse geometrico-static problem namely by using (a) shooting methods
to obtain a numerical solution, (b) an elliptic method to find a quasi-analytical
solution, and (c) the Corde model to perform further model analysis.
The performances of each of the studied methods are evaluated and their limits
are highlighted.
This thesis is divided as follows. Chapter one gives the introduction on the
field of the continuum robotics and introduce the parallel continuum robots that is
studied in this work. Chapter two describe the geometrico-static problem and gives
the mathematical description of this problem. Chapter three explains the numerical
approach with the shooting method and chapter four introduce the quasi-analytical
solution. Then, Chapter five introduce the analytic method inspired by the Corde
model and chapter six gives the conclusions of this work.
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Branke, Dominik. "Homogenisierungsmethode für den Übergang vom Cauchy- zum Cosserat-Kontinuum." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-106300.
Повний текст джерелаАнотація:
Diese Arbeit liefert ein dreidimensionales numerisches Homogenisierungskonzept, welches beim Übergang von der Mikro- zur Makroskala einen Wechsel in der Kontinuumsbeschreibung beinhaltet. Während für die Beschreibung der Makroskala das verallgemeinerte Cosserat-Kontinuum verwendet wird, basiert die Mikroskala auf der klassischen Cauchy-Theorie. Um das homogene Cosserat-Ersatzmaterial im Rahmen numerischer Simulationen nutzen zu können, erfolgt die Implementierung geeigneter Finiter Elemente in das Programmsystem Abaqus und deren Verifikation. Neben der Diskussion der bei der Homogenisierung beobachteten Effekte werden anhand eines idealisierten Modells eines biaxialverstärkten Mehrlagengestrickes die Vorteile gegenüber der klassischen Herangehensweise aufgezeigtThis contribution provides a threedimensional homogenization approach which includes the switch of the continuum theory during the scale transition. Whereas the microscopic scale is described in the framework of the classical Cauchy theory, the macroscopic scale is based on the generalized Cosserat continuum. In order to use the obtained homogeneous Cosserat material, suitable finite elements are implemented in the commercial program system Abaqus followed by an appropriate verification. Beside the discussion of the arising effects the advantages of this approach compared to the classical procedure are shown by means of an idealized model of a biaxial woven fabric
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Gulib, Fahad. "Constitutive models and finite elements for plasticity in generalised continuum theories." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33277.
Повний текст джерелаАнотація:
The mechanical behaviour of geomaterials (e.g. soils, rocks and concrete) under plastic deformation is highly complex due to that fact that they are granular materials consisting of discrete non-uniform particles. Failure of geomaterials is often related to localisation of deformation (strain-localisation) with excessive shearing inside the localised zones. The microstructure of the material then dominates the material behaviour in the localised zones. The formation of the localised zone (shear band) during plastic deformation decreases the material strength (softening) significantly and initiates the failure of the material. There are two main approaches to the numerical modelling of localisation of deformation in geomaterials; discrete and continuum. The discrete approach can provide a more realistic material description. However, in the discrete approach, the modelling of all particles is complicated and computationally very expensive for a large number of particles. On the other hand, the continuum approach is more flexible, avoids modelling the interaction of individual particles and is computationally much cheaper. However, classical continuum plasticity models fail to predict the localisation of deformation accurately due to loss of ellipticity of the governing equations, and spurious mesh-dependent results are obtained in the plastic regime. Generalised plasticity models are proposed to overcome the difficulties encountered by classical plasticity models, by relaxing the local assumptions and taking into account the microstructure-related length scale into the models. Among generalised plasticity models, Cosserat (micropolar) and stain-gradient models have shown significant usefulness in modelling localisation of deformation in granular materials in the last few decades. Currently, several elastoplastic models are proposed based on Cosserat and strain-gradient theories in the literature. The individual formulation of the models has been examined almost always in isolation and are paired with specific materials in a mostly arbitrary fashion. Therefore, there is a lack of comparative studies between these models both at the theory level and in their numerical behaviour, which hinders the use of these models in practical applications. This research aims to enable broader adoption of generalised plasticity models in practical applications by providing both the necessary theoretical basis and appropriate numerical tools. A detailed comparison of some Cosserat and strain-gradient plasticity models is provided by highlighting their similarities and differences at the theory level. Two new Cosserat elastoplastic models are proposed based on von Mises and Drucker- Prager type yield function. The finite element formulations of Cosserat and strain-gradient models are presented and compared to better understand their advantages and disadvantages regarding numerical implementation and computational cost. The finite elements and material models are implemented into the finite element program ABAQUS using the user element subroutine (UEL) and an embedded user material subroutine (UMAT) respectively. Cosserat finite elements are implemented with different Cosserat elastoplastic models. The numerical results show how the Cosserat elements behaviour in the plastic regime depends on the models, interpolation of displacement and rotation and the integration scheme. The effect of Cosserat parameters and specific formulations on the numerical results based on the biaxial test is discussed. Two new mixed-type finite elements as well as existing ones (C1, mixed-type and penalty formulation), are implemented with different strain-gradient plasticity models to determine the numerical behaviour of the elements in the plastic regime. A detailed comparison of the numerical results of Cosserat and strain-gradient elastoplastic models is provided considering specific strain-localisation problems. Finally, some example problems are simulated with both the Cosserat and strain-gradient models to identify their applicability.
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MENDONZA, ANGELA ROCIO BAYONA. "ANALYSIS OF INSTABILITY OF OIL WELLS ASSOCIATED WITH THE SAND PRODUCTION THROUGH A MODEL OF THE COSSERAT CONTINUUM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4631@1.
Повний текст джерелаАнотація:
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOA produção de areia é um dos mais freqüentes e graves problemas observados durante a produção de um poço de petróleo, completado em arenitos mal consolidados. Este fenômeno pode causar obstrução do poço, abrasão dos equipamentos de elevação e de superfície, colapso do revestimento e problemas ambientais derivados da disposição em superfície das areias contaminadas. Por outro lado, em reservatórios de baixa produtividade que produzem óleo de alta viscosidade, uma limitada produção de areia incrementa a produtividade do poço. Nos estudos para previsão da produção de areia é de fundamental importância definir-se um modelo constitutivo capaz de reproduzir o comportamento tensão-deformação do arenito e os mecanismos de ruptura que provocam instabilidade do poço. Este é o tema central desta tese. Em especial, o trabalho procurou explorar modelos constitutivos baseados em meios contínuos de Cosserat. Uma justificativa para isto está relacionada ao fato de experimentos demonstrarem a influência da microestrutura nos processos de ruptura que ocorrem na vizinhança do poço. O modelo utilizado foi o elastoplástico de Bogdanova-Bontcheva & Lippmann (1975) incorporando as leis de fluxo associada e não associada. Inicialmente são definidos alguns conceitos básicos relevantes ao entendimento do fenômeno de produção de sólidos. Uma revisão da teoria dos meios contínuos generalizados de Cosserat é apresentada e em seguida é discutido o modelo elastoplástico de Bogdanova- Bontcheva e Lippmann com detalhes das implementações computacionais necessárias. Finalmente, são feitas análises de geometrias de poços, procurando-se identificar os mecanismos de ruptura que provocam instabilidade e que são uma potencial fonte de produção de areia.
Sand production is one of the most frequent and serious problems observed during the production of an oil well completed in weak sandstones. This phenomenon can cause wellbore plugging, surface and rise equipment abrasion, casing collapse and environmental problems derived from the disposal in surface of contaminated sands. On the other hand, for reservoirs of low productivity, that produce oil of high viscosity, a limited sand production increase the productivity of the well. In the studies for sand production prediction, it is of basic importance to define a consitutive model capable of reproducing the stress-strain behaviour of the sandstones and the failure mechanisms that causes wellbore instability. This is the central focus of the present work. In order to represent the behaviour of the rock masses, models based in Cosserat continuum were used. Elastoplastic models (associated/not associated) under that theory (Bogdanova-Bontcheva & Lippmann) were implemented. Initially, basic concepts related to the understanding of the phenomenon of solid production are presented. A review of the theory of generalized Cosserat continuum is presented, the elastoplastic model of Bogdanova-Bontcheva and Lippmann is described, together with details of the computational implementations. Finally, analyses of well geometries with the implemented Cosserat based elastoplastic models are shown,identifying the failure mechanisms.
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Rattez, Hadrien. "Couplages thermo-hydro-mécanique et localisation dans les milieux de Cosserat : application à l'analyse de stabilité du cisaillement rapide des failles." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1181/document.
Повний текст джерелаАнотація:
Les matériaux soumis à de grandes déformations présentes pour la plupart l’apparition de déformations inélastiques. Ce phénomène est souvent accompagné d’une localisation des déformations dans une zone étroite, précurseur de la rupture. Un cas particulier, mais très fréquent, est les bandes de cisaillement qui apparaissent pour beaucoup de géomatériaux. Ces bandes peuvent être rencontrées à des échelles allant de l’échelle kilométrique pour les zones de subduction à l’échelle micrométrique à l’intérieur des zones de faille. Etudier et modéliser la création de ces zones d’instabilité est fondamental pour décrire la rupture des géomatériaux et des phénomènes associés comme les glissements sismiques dans les zones de faille mature de la lithosphère. Les conditions de pression, de température, l’interaction de l’eau interstitielle avec un matériau finement fracturé conduisent à l’apparition de multiples processus physiques impliqués dans les glissements sismiques. Dans ce travail, nous nous attachons à modéliser la création de bandes de cisaillement à l’intérieur des gouges de faille en prenant en compte l’effet de la microstructure par l’intermédiaire des milieux continus de Cosserat, ainsi que les couplages thermo-hydro-mécanique. L’utilisation de la théorie de Cosserat permet non seulement de régulariser le problème de localisation des déformations par l’introduction d’une longueur interne dans les lois constitutives, mais en même temps de prendre en compte l’effet de la microstructure. Deux approches sont employées pour étudier le système d’équations couplées aux dérivées partielles non linéaires : L’analyse de stabilité linéaire et la méthode des éléments finis. L’analyse de stabilité linéaire permet d’examiner les conditions d’apparitions d’instabilités pour un système mécanique avec des couplages multi-physiques. Par ailleurs, des considérations sur les perturbations appliquées au système permettent aussi de déterminer l’épaisseur de la zone de cisaillement, un paramètre clé pour la compréhension du mécanisme mécanique des failles. Ces estimations sont confirmées par l’intégration numérique pour des déformations restant dans une gamme donnée. Elles sont confrontées aux observations expérimentales et in situ et présentent une bonne corrélation. D’autre part, les simulations numériques permettent d’obtenir la réponse mécanique de la gouge de faille et de donner des informations sur l’influence des différents couplages dans le budget énergétique d’un tremblement de terreWhen materials are subjected to large deformations, most of them experience inelastic deformations. It is often accompanied by a localization of these deformations into a narrow zone leading to failure. One particular case of strain localization is the formation of shear bands which are the most common patterns observed in geomaterials. In geological structures, they appear at very different scales, from kilometer scale for subduction zones, to micrometric scale inside fault cores. Studying their occurrence and evolution is of key importance to describe the failure of geomaterials and model seismic slip for mature crustal faults. The pressure and temperature conditions in these faults and the interaction with the pore water inside a highly fractured materials highlight the importance of different physical processes involved in the nucleation of earthquakes. In this thesis, we study the occurrence and evolution of shear bands inside fault gouges taking into account the material microstructure by resorting to elastoplastic Cosserat continua and also the effect of thermo-hydro mechanical couplings. The use of Cosserat theory introduces information about the gouge microstructure, namely the grain size, and permits to regularize the mathematical problem of in the post-localization regime by introducing an internal length into the constitutive equations. Two approaches are used to study the coupled non-linear partial differential set of equations: linear stability analysis and finite element simulations. Linear stability analysis allows to study the occurrence of localized deformation in a mechanical system with multi-physical couplings. Considerations on the dominant wave length of the perturbations permit also to determine the width of the localized zone. This shear band thickness is confirmed by numerical integration in the post-localization regime for a certain range of deformation. The obtained widths of the localized zone are key parameters for understanding fault behavior, are in agreement with experimental and field observations. Moreover, numerical finite element computations enable to model the mechanical response of a fault gouge during seismic slip and give insights into the influence of various physical couplings on the energy budget
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Grbčić, Sara. "Linked interpolation and strain invariance in finite-element modelling of micropolar continuum." Thesis, Compiègne, 2018. http://www.theses.fr/2018COMP2454.
Повний текст джерелаАнотація:
Au cœur de cette thèse est une théorie de continuum alternatif connue comme la théorie micropolaire, qui est développée pour décrire des phénomènes lesquels on ne peut pas décrire en utilisant la théorie classique. Dans cette théorie, en complément du champ de déplacement, il existe aussi un autre champ indépendant, celui de microrotation, et afin de pouvoir décrire complètement un tel matériau, six paramètres des matériaux sont nécessaires. Dans le cadre de la modélisation par éléments finis, nouveaux éléments fondés sur la théorie micropolaire dans les régimes linéaire et géométriquement non linéaire sont développés. Dans le cadre de l'analyse linéaire, les problèmes bi- et tri-dimensionnels sont analysés. En 2D, les nouvelles familles des éléments triangulaires et quadrilatères sont développés avec l'interpolation liée des champs cinématiques. Ensuite, la forme faible est étendue aux 3D, et un élément fini hexaédrique du premier ordre, avec le champ de déplacement enrichi avec des modes incompatibles est dérivé. Il est constaté que l'interpolation liée et les modes incompatibles améliore la précision par rapport à la précision des éléments finis micropolaires conventionnels. Dans le part non-linéaire, les éléments de premier et deuxième ordre avec l'interpolation conventionnelle sont développés. Pour tester la performance des éléments présentés, une solution analytique non-linéaire de la flexion pure est dérivée. Il est observé que les éléments convergent vers la solution dérivée. Les éléments sont testés sur les autres exemples où la dépendance du sentier et l'invariance de déformation sont détectés. Une procédure pour résoudre ces anomalies est présentéeAt the core of this thesis is an alternative continuum theory called the micropolar (Cosserat) continuum theory, developed in order to describe the phenomena which the classical continuum theory is not able to describe. In this theory, in addition to the displacement field, there also exists an independent microrotation field and, in order to completely describe such a material, six material parameters are needed. In the framework of the finite-element method, new finite elements based on the micropolar continuum theory in both linear and geometrically non-linear analysis are developed using the displacement-based approach. In the linear analysis, both two- and three-dimensional set-ups are analysed. In 2D new families of triangular and quadrilateral finite elements with linked interpolation of the kinematic fields are derived. In order to assure convergence of the derived finite elements, they are modified using the Petrov-Galerkin approximation. Their performance is compared against existing conventional micropolar finite elements on a number of micropolar benchmark problems. It is observed that the linked interpolation shows enhanced accuracy in the bending test when compared against the conventional Lagrange micropolar finite element. Next, the weak formulation is extended to 3D and a first-order hexahedral finite element enhanced with the incompatible modes is derived. The element performance is assessed by comparing the numerical results against the available analytical solutions for various boundary value problems, which are shown to be significant for the experimental verification of the micropolar material parameters. It is concluded that the proposed element is highly suitable for the validation of the methodology to determine the micropolar material parameters. In the non-linear part, first- and second-order geometrically nonlinear hexahedral finite elements with Lagrange interpolation are derived. In order to test the performance of the presented finite elements, a pure-bending non-linear micropolar analytical solution is derived. It is observed that the elements converge to the derived solution. The elements are tested on three additional examples where the path-dependence and strain non-invariance phenomena are detected and assessed in the present context. A procedure to overcome the non-invariance anomaly is outlined
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Lasota, Tomáš. "Computational Modelling of Mechanical Behaviour of "Elastomer-Steel Fibre" Composite." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2013. http://www.nusl.cz/ntk/nusl-234188.
Повний текст джерелаАнотація:
Tato práce se zabývá výpočtovými simulacemi zkoušek jednoosým tahem a tříbodovým ohybem kompozitního vzorku složeného z elastomerové matrice a ocelových výztužných vláken orientovaných pod různými úhly, jakož i jejich experimentální verifikací. Simulace byly provedeny pomocí dvou různých modelů - bimateriálového a unimateriálového výpočtového modelu. Při použití bimateriálového modelu, který detailně zohledňuje strukturu kompozitu, tzn. pracuje s matricí a jednotlivými vlákny, je zapotřebí vytvořit model každého vlákna obsaženého v kompozitu, což přináší řadu nevýhod (pracná tvorba výpočtového modelu, řádově větší množství elementů potřebných k diskretizaci v MKP systémech a delší výpočetní časy). Na druhé straně v unimateriálovém modelu se nerozlišují jednotlivá vlákna, pracuje se pouze s kompozitem jako celkem tvořeným homogenním materiálem a výztužný účinek vláken je zahrnut v měrné deformační energii. Porovnání experimentů se simulacemi ukázalo, že bimateriálový model je v dobré shodě s experimenty, na rozdíl od unimateriálového modelu, který je schopen poskytnou odpovídající výsledky pouze v případě tahového namáhání. Z tohoto důvodu byl hledán způsob, který by umožnil rozšířit unimateriálový model o ohybovou tuhost výztužných vláken. V roce 2007 Spencer a Soldatos publikovali rozšířený unimateriálový model, který je schopen pracovat nejen s tahovou, ale i ohybovou tuhostí vlákna. Představený obecný model je však založen na Cosseratově teorii kontinua a jeho praktické využití je pro jeho složitost nemožné. Proto byl vytvořen zjednodušený model (částečně podle Spencera a Soldatose) s vlastní navrženou formou měrné deformační energie. Za účelem ověření nového unimateriálového modelu s ohybovou tuhostí vláken byly odvozeny všechny potřebné rovnice a byl napsán vlastní konečno-prvkový řešič. Tento řešič je založen na Cosseratově teorii kontinua a obsahuje zmíněný anizotropní hyperelastický unimateriálový model zahrnující ohybovou tuhost vláken. Vzhledem k tomu, že v případě Cosseratovy teorie jsou při výpočtu potřebné i druhé derivace posuvů, bylo nutné použít tzv. C1 prvky, které mají spojité jak pole posuvů, tak jejich prvních derivací. Nakonec byly provedeny nové simulace s využitím vlastního řešiče, které ukazují, že tuhost vláken lze u nového unimateriálového modelu řídit odpovídající materiálovou konstantou. V závěru práce je pak diskutováno, zda je nový unimateriálový model s ohybovou tuhostí schopen poskytnout stejné výsledky jako model bimateriálový, a to jak při tahovém tak i ohybovém namáhání kompozitního vzorku.
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Riahi, Dehkordi Azadeh. "3D Finite Element Cosserat Continuum Simulation of Layered Geomaterials." Thesis, 2008. http://hdl.handle.net/1807/17250.
Повний текст джерелаАнотація:
The goal of this research is to develop a robust, continuum-based approach for a three-dimensional, Finite Element Method (FEM) simulation of layered geomaterials. There are two main approaches to the numerical modeling of layered geomaterials; discrete or discontinuous techniques and an equivalent continuum concept.
In the discontinuous methodology, joints are explicitly simulated. Naturally, discrete techniques provide a more accurate description of discontinuous materials. However, they are complex and necessitate care in modeling of the interface. Also, in many applications, the definition of the input model becomes impractical as the number of joints becomes large. In order to overcome the difficulties associated with discrete techniques, a continuum-based approach has become popular in some application areas. When using a continuum model, a discrete material is replaced by a homogenized continuous material, also known as an 'equivalent continuum'. This leads to a discretization that is independent of both the orientation and spacing of layer boundaries. However, if the layer thickness (i.e., internal length scale of the problem) is large, the classical continuum approach which neglects the effect of internal characteristic length can introduce large errors into the solution.
In this research, a full 3D FEM formulation for the elasto-plastic modeling of layered geomaterials is proposed within the framework of Cosserat theory. The effect of the bending stiffness of the layers is incorporated in the matrix of elastic properties. Also, a multi-surface plasticity model, which allows for plastic deformation of both the interfaces between the layers and intact material, is introduced. The model is verified against analytical solutions, discrete numerical models, and experimental data. It is shown that the FEM Cosserat formulation can achieve the same level of accuracy as discontinuous models in predicting the displacements of a layered material with a periodic microstructure. Furthermore, the method is capable of reproducing the strength behaviour of materials with one or more sets of joints. Finally, due to the incorporation of layer thickness into the constitutive model, the FEM Cosserat formulation is capable of capturing complicated failure mechanisms such as the buckling of individual layers of material which occur in stratified media.
Книги з теми "Continuum micromorphe de Cosserat"
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Vardoulakis, Ioannis. Cosserat Continuum Mechanics. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-95156-0.
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Rubin, M. B. Cosserat theories: Shells, rods, and points. Dordrecht: Kluwer Academic Publishers, 2000.
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W. L. A. H. Van den Broek. Numerical modelling of plane strain compression tests using a classical and cosserat continuum. Manchester: UMIST, 1996.
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(Deceased), Ioannis Vardoulakis. Cosserat Continuum Mechanics: With Applications to Granular Media. Springer, 2018.
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(Deceased), Ioannis Vardoulakis. Cosserat Continuum Mechanics: With Applications to Granular Media. Springer, 2019.
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Mechanics of Generalized Continua: Proceedings of the IUTAM-Symposium on The Generalized Cosserat Continuum and the Continuum Theory of Dislocations. . . and Stuttgart 1967. Springer, 2014.
Знайти повний текст джерелаЧастини книг з теми "Continuum micromorphe de Cosserat"
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Vardoulakis, Ioannis. "Cosserat Fluids." In Cosserat Continuum Mechanics, 121–50. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_8.
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Vardoulakis, Ioannis. "Cosserat Continuum Kinematics." In Cosserat Continuum Mechanics, 33–57. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_3.
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Vardoulakis, Ioannis. "Cosserat Continuum Statics." In Cosserat Continuum Mechanics, 59–73. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_4.
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Vardoulakis, Ioannis. "Cosserat Continuum Dynamics." In Cosserat Continuum Mechanics, 75–87. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_5.
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Vardoulakis, Ioannis. "Cosserat Continuum Energetics." In Cosserat Continuum Mechanics, 89–97. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_6.
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Ehlers, Wolfgang, and Sami Bidier. "Cosserat Media." In Encyclopedia of Continuum Mechanics, 436–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_149.
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Ehlers, Wolfgang, and Sami Bidier. "Cosserat Media." In Encyclopedia of Continuum Mechanics, 1–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53605-6_149-1.
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Vardoulakis, Ioannis. "Cosserat-Elastic Bodies." In Cosserat Continuum Mechanics, 99–119. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_7.
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Vardoulakis, Ioannis. "Rigid-Body Mechanics and Motors." In Cosserat Continuum Mechanics, 5–32. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_2.
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Vardoulakis, Ioannis. "Mechanics of Discrete Granular Media." In Cosserat Continuum Mechanics, 151–79. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95156-0_9.
Повний текст джерелаТези доповідей конференцій з теми "Continuum micromorphe de Cosserat"
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PASTERNAK, E., and H. B. MÜHLHAUS. "LARGE DEFORMATION COSSERAT CONTINUUM MODELLING OF GRANULATE MATERIALS." In Proceedings of the Third Australasian Congress on Applied Mechanics. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777973_0063.
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Grekova, E. F., and G. C. Herman. "Wave Propagation in Rocks Modeled as Reduced Cosserat Continuum." In 66th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2004. http://dx.doi.org/10.3997/2214-4609-pdb.3.p098.
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COURTEAU-GODMAIRE, HUBERT, ANOUSH POURSARTIP, and REZA VAZIRI. "BENDING SIMULATION OF PRE-GELLED COMPOSITES USING AN EXPLICIT COSSERAT CONTINUUM MODEL." In Thirty-sixth Technical Conference. Destech Publications, Inc., 2021. http://dx.doi.org/10.12783/asc36/35844.
Повний текст джерелаАнотація:
Forming simulation of uncured pre-preg can be made more efficient with the use of dedicated finite elements tailored for soft, layered media. These elements are based on the Cosserat continuum theory that introduces a rotational degree of freedom at each node within standard solid elements. In this study, a Cosserat element is developed within a 2D non-linear explicit finite element framework that uses the Carrera Unified Formulation for its spatial discretization. Two benchmark case studies involving bending deformations are presented as the verification of the developed model. It is demonstrated that similar accuracy of predictions can be achieved with much coarser meshes of Cosserat elements than the equivalent classical finite element models consisting of multi-layer stacks of solid elements.
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Hu, Zhaolong, and Hongxiang Tang. "A Transversely Isotropic Cosserat Continuum Model and Its Numerical Application." In Second International Conference on Geotechnical and Earthquake Engineering. Reston, VA: American Society of Civil Engineers, 2013. http://dx.doi.org/10.1061/9780784413128.064.
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Lalin, Vladimir, and Elizaveta Zdanchuk. "Reduced cosserat continuum as a possible model for granular medium." In Proceedings of the International Conference „Innovative Materials, Structures and Technologies”. Riga: Riga Technical University, 2014. http://dx.doi.org/10.7250/iscconstrs.2014.15.
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Sharbati, Ehsan, and Reza Naghdabadi. "Large Deformation Analysis of Elastic Cosserat Continua by FEM." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95288.
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Based on the non linear terms appearing in the strain tensor in classical continuum mechanics, two expressions for large strain in the Cosserat continuum are proposed. The generalized form of principal of virtual work together with the constitutive equations for an isotropic elastic Cosserat continuum are used to derive the finite element formulations for elastic large deformation analysis based on the Cosserat theory. The finite element formulations are then applied to a four-node quadrilateral element with three degrees of freedom at each node including two translational and one rotational degrees of freedom. The tension of a semi-infinite plate with a circular whole in the center is solved using the Cosserat finite element formulation and the results are compared with those obtained by the classical theory. Also, pure bending and shear of a cantilever beam are done and the differences of the results obtained based on the two proposed formulations of large strains are investigated.
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Ghasvari Jahromi, H., G. Atefi, A. Moosaie, S. Hormozi, and H. Afshin. "Analytical Solution of Turbulent Couette Flow by Cosserat Continuum Model and Gradient Theory." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98431.
Повний текст джерелаАнотація:
In present paper the theory of the micropolar fluid based on a Cosserat continuum model has been applied for analysis of Couette flow. The obtained results for the velocity field have been compared with known results from experiments done by Reichardt at Max Plank institute for fluids in Gottingen [1,2] and analytical solution of the problem from Gradient theory by Alizadeh [3]. The boundary condition used here was the no slip one and Trostel’s slip boundary condition [4]. A good agreement between experimental results and the results of the problem for Reynolds near 18000 has beeen found. A new dimensionless number introduced that indicates the theoretical relation between cosserat theory and slip theory and their interaction.
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Grekova, E. F., and G. C. Herman. "Wave Propagation in Rocks Modeled as Reduced Cosserat Continuum with Weak Anisotropy." In 67th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2005. http://dx.doi.org/10.3997/2214-4609-pdb.1.p164.
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Congwen Peng, Xiangguo Kong, and Chengxiang Xu. "Numerical implementation of pressure-dependent elasto-plastic cosserat continuum model in ABAQUS." In 2011 Second International Conference on Mechanic Automation and Control Engineering (MACE). IEEE, 2011. http://dx.doi.org/10.1109/mace.2011.5988563.
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Ghasvari-Jahromi, H., Gh Atefi, A. Moosaie, and S. Hormozi. "Analytical Solution of Turbulent Problems Using Governing Equation of Cosserat Continuum Model." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15837.
Повний текст джерелаАнотація:
In present paper the theory of the micropolar fluid based on a Cosserat continuum model has been applied for analysis of Couette flow and turbulent flow through rough pipes. The obtained results for the velocity field have been compared with known results from experiments done by Reichardt at Max Plank institute for fluids in Gottingen [1,2] and analytical solution of the problem from Gradient theory by alizadeh[3] for couette problem and with known results from experiments done by Nikuradse (1932). the boundary condition used here was the no slip one and Trostel's slip boundary condition[4].a good agreement between experimental results and the results of the problem for Reynolds near 18000 has beeen found in the couette case also in this case A new dimensionless number introduced that indicates the theoretical relation between cosserat theory and slip theory and their interaction. The solution has been performed for a Reynolds number of 106 for pipes with different values of roughness and the validity analysis approved by the results of Nikuradse's experiments.