Academic literature on the topic 'Cosserat micromorphic continuum'

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. .

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.

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.

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.

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 général
During 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