In the literature, there are various material models proposed so as to model the constitutive behavior of hyperelastic materials for example, St. Venant-Kirchho_ model, Mooney-Rivlin model etc. The stability of such material models under various states of deformation is of important concern, and generally stability analysis is conducted in homogeneous states of deformation. Within hyperelasticity, instabilities can be broadly classified as geometrical and material types. Geometrical instabilities such as buckling, symmetric bifurcation etc. are of physical origin, and lead to multiple solutions at critical stretch. Material instability is a aw in the material model and leads to unphysical solutions at the onset. It is required that the constitutive model should be materially stable i.e., should not give unphysical results, and be able to predict correctly the onset of geometrical instabilities. Certain constitutive restrictions proposed in the literature are inadequate to characterize such instabilities. In the work, we propose stability criteria which will characterize geometrical as well as material instabilities. A new elasticity tensor is defined, which is found to characterize material instability adequately. In order to investigate the validity of proposed stability criteria, three important constitutive models of hyperelasticity viz., St. Venant-Kirchho_, compressible Mooney-Rivlin and compressible Ogden models are investigated for stability.

This thesis consists of two parts. The first part explores a 2-d edge dislocation model to demonstrate characteristics of Field Dislocation Mechanics (FDM) in modeling single and collective behavior of individual dislocations. The second work explores the possibility of modelling adiabatic shear bands propagation within the timespace averaged framework of Mesoscopic Field Dislocation Mechanics (MFDM). It is demonstrated that FDM reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. The explored questions include the existence of a Peierls stress in translationally-invariant media, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics. A variety of dislocation pile-up problems are studied, primarily complementary to what can be dealt by existing classical pile-up models. In addition, the model suggests the possibility that the tip of a shear band can be modelled as a localized spatial gradient of elastic distortion with the dislocation density tensor in continuum dislocation mechanics; It is demonstrated that the localization can be moved by its theoretical driving force and forms a diffuse traveling band tip, thereby extending the thin layer of the deformation band. A 3-d, parallel finite element framework of MFDM is developed in a geometrically nonlinear context for the purpose of modelling shear bands. The numerical formulations and algorithm are presented in detail. Constitutive models appropriate for single crystal plasticity response and J2 plasticity with thermal softening are implemented.

Hard ceramic films of micrometric thickness deposited on a soft metallic substrate have ushered in a new era in the fabrication of structural, tribological, microelectronic and optical components. The mechanical performance of these components is however critically dependent on the strength and toughness of these films as well as on those of the film-substrate interface. Recent studies have shown that cylindrical and radial cracks can propagate through the film during nanoindentation tests with spherically tipped and pointed indenters, resulting in steps in the load versus displacement curve. In this thesis, the mechanics of fracture of thin hard films bonded to soft substrates, during nanoindentation is studied by carrying out finite element analyses. The role of plastic yielding in the substrate on the above issue is examined. Another important objective of this work is to propose a method by which finite element simulations can be employed to interpret nanoindentation test results and yield information related to the fracture behaviour of hard films. To this end, axisymmetric finite element analyses of spherical nanoindentation of a TiN film of thickness t = 1 //m, on a steel substrate are carried out. Numerical algorithms for large deformation, contact simulation and computation of energy release rate are employed in the analyses. The film is assumed to be linear elastic, whereas, an elastic-plastic constitutive model is used for the substrate. A nanoindentation analysis of the uncracked film is first carried out. The development of plastic yielding in the substrate and its influence on the load P versus penetration h characteristics is examined. The stress fields around the indenter for different depths of indentation are studied. The results show that the radial stress attains a tensile peak at the film surface, just outside the indented zone. However, it becomes compressive with increasing distance below the surface. Interestingly, a tensile radial stress prevails at the film-substrate interface at large indentation depth. The shear stress increases to a peak value at a distance of 0.052 to OAt below the film surface depending upon the radial location and then reduces. Next, circumferential cracks extending downwards from the film surface are introduced at different radial distances R from the axis of symmetry. Finite element analyses are carried out till the indented zone extends almost up to the crack surface. The energy release rate J is computed as a function of indentation depth for different crack lengths c (in the range from O.lt to 0.9t). The results show that shallow cracks are essentially under Mode II loading with closure of crack faces caused by compressive radial stresses. However, a mixed-mode state prevails if the crack length is large (c > 0.62), with crack faces opening out due to tensile radial stress near the film-substrate interface. The variation of J with c/t for cracks located at different radial distances R is examined. It is found that for small R, there is a decreasing branch in the J versus c variation between c = 0.2i to 0.75£ which indicates that crack extension in this range will be stable. On the other hand, for large R, J increases monotonically with c/t which implies that unstable fracture of the full film thickness will occur following crack initiation. A composite nomogram is generated in the P — h plane where constant J lines are plotted along with load-displacement curves for different crack lengths. If now a nanoindentation (experimental) load-displacement behaviour is superimposed on this nomogram, the initial crack length (of a pre-existing flaw), the final crack length and fracture energy of the film can be inferred. In the last part of the thesis, the effect of the substrate yield strength on the indentation mechanics is studied. It is found that upon decreasing the yield strength, the load at a given indentation depth decreases while the residual depth at unloading increases. Also, the energy release rate for a given radial location and crack length reduces considerably at large depths of indentation.

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The objectives of this work are to discuss multiscale models that are used to characterize the constitutive relations of the granular composite materials with dual functions. This is accomplished by the use of ab initio methods to obtain the constitutive relations of the structural energetic materials without conducting tests. First, it is necessary to study the quantum many body problem to quantitatively determine the internal energy of the material when subjected to different strain conditions. It is impossible to obtain an exact solution to the quantum many body problem that is modeled by the Schrödinger's equations with the current technology. It is possible to solve these equations approximately by the density functional theory which yields only energies at absolute 0ºK. Thus it becomes necessary to add both the lattice thermal contributions and electron thermal contribution. Then, resulting energy is used to bridge to the continuum level and obtain the constitutive equations. This is the procedure that is used in this work. The issues of the constitutive equations form the focus of this thesis. More specifically, the scope of the thesis is further restricted to analyze the constitutive equations of specific mixtures of nickel, aluminum with PTFE or Teflon as the binder. It is to be noted that the equations of state forms only a part of the complete constitutive relationships. This thesis presents solutions to the following problems: (1) Determination of the thermodynamically complete equation of state of the binder and the energetic material PTFE or Teflon, from ab initio methods based on the density functional theory. (2) Determination of the equations of state of the granular composite or the mixture of nickel, aluminum and PTFE from ab initio methods. (3) Determination of the complete constitutive equation of aluminum, from ab initio methods, under conditions of finite deformations, with principle of objectivity, material symmetry conditions and polyconvexity of the strain energy. All results are compared to test results whenever they are available.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18241号 / 工博第3833号 / 新制||工||1587(附属図書館) / 31099 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 木村 亮, 教授 三村 衛, 准教授 木元 小百合 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This thesis focuses on calculation of finite and progressive deformation in different tectonic scales using 2D numerical models with application to natural cases. Essentially, two major tectonic areas have been covered: a) salt tectonics and b) upper mantle deformation due to interaction between the lithosphere and asthenosphere. The focus in salt tectonics lies on deformation within down-built diapirs consisting of a source layer feeding a vertical stem. Three deformation regimes have been identified within the salt: (I) a squeezing channel flow underneath the overburden, (II) a corner flow underneath the stem, and (III) a pure channel flow within the stem. The results of the model show that the deformation pattern within the stem of a diapir (e.g. symmetric or asymmetric) can reveal information on different rates of salt supplies from the source layer (e.g. observed in Klodowa-diapir, Poland). Composite rock salt rheology results in strong localization and amplification of the strain along the salt layer boundaries in comparison to Newtonian rock salt. Flow and fold structures of passive marker lines are directly correlated to natural folds within a salt diapir. In case of the upper mantle, focus lies on deformation and resulting lattice preferred orientation (LPO) underneath an oceanic plate. Sensitivity of deformation and seismic anisotropy on rheology, grain size (d), temperature (T), and kinematics (v) has been investigated. The results of the model show that the mechanical lithosphere-asthenosphere boundary is strongly controlled by T and less so by v or d. A higher strain concentration within the asthenosphere (e.g. for smaller potential mantle temperatures, higher plate velocities, or smaller d) indicates a weaker coupling between the plate and the underlying mantle, which becomes stronger with the age of the plate. A Poiseuille flow within the asthenosphere, significantly affects the deformation and LPO in the upper mantle. The results of the model show, that deformation in the upper mantle at a certain distance away from the ridge depends on the absolute velocity in the asthenosphere. However, only in cases of a driving upper mantle base does the seismic anisotropy and delay times reach values within the range of natural data.

Les composites élastomères sont actuellement utilisés dans de nombreuses applications commerciales et ont montré de grandes promesses pour l'utilisation dans les nouvelles technologies. Cela soulève la pratique, ainsi que théorique nécessaire pour comprendre le lien entre la microstructure sous-jacente de composites en élastomère et de leurs propriétés mécaniques et physiques, et comment celui-ci peut être améliorée avec des changements dans l'ancienne. Dans ce contexte, l'objectif principal de cette thèse est le développement d'une analyse, le cadre homogénéisation non linéaire pour déterminer la réponse globale des composites élastomères soumis à des déformations finies. Les comptes-cadre pour l'évolution de la microstructure sous-jacente, ce qui entraîne des changements dans la géométrie finie induite par la charge appliquée. Ce point est essentiel que l'évolution de la microstructure peut avoir un assouplissement significatif géométrique (ou raidissage) effet sur la réponse globale du matériau, qui, à son tour, peut conduire à l'élaboration éventuelle d'instabilités macroscopiques. Le concept principal derrière la méthode d'homogénéisation non linéaire proposé est la construction de principes variationnels appropriés en utilisant l'idée d'un "portail composite linéaire», qui a finalement permettre la conversion des estimations disponibles homogénéisation linéaire dans les estimations analytiques pour la grande déformation de réponse global de l' non linéaire des composites en élastomère. Cette thèse comprend des applications de la théorie proposée pour les différentes classes des élastomères renforcés et poreux aléatoire et des microstructures périodiques. Une analyse complète du comportement efficace, l'évolution de la microstructure et le développement d'instabilités macroscopiques est prévu pour toutes ces applications.

L’adaptation des surfaces pour des fonctions prédéterminées par le choix des matériaux métalliques ou des couches minces ayant des propriétés mécaniques avancées peut potentiellement permettre de réaliser des nouvelles applications à petites échelles. Concevoir de telles applications utilisant des nouveaux matériaux nécessite en premier lieu la connaissance des propriétés mécaniques des matériaux ciblés à l’échelle microscopique et nanoscopique. Une méthode souvent appliquée pour caractériser les matériaux à petites échelles est la nanoindentation, qui peut être vue comme une mesure de dureté à l’échelle nanoscopique. Ce travail présente une contribution relative à l'interprétation des résultats de la nanoindentation, qui fait intervenir un grand nombre de phénomènes physiques couplés à l'aide de simulations numériques. A cette fin une approche interdisciplinaire, adaptée aux phénomènes apparaissant à petites échelles, et située à l’intersection entre la physique, la mécanique et la science des matériaux a été utilisée. Des modèles numériques de la nanoindentation ont été conçus à l'échelle atomique (modèle discret) et à l'échelle des milieux continus (méthode des éléments finis), pour étudier le comportement du nickel pur. Ce matériau a été choisi pour ses propriétés mécaniques avancées, sa résistance à l'usure et sa bio-compatibilité, qui peuvent permettre des applications futures intéressantes à l'échelle nanoscopique, particulièrement dans le domaine biomédical. Des méthodes avancées de mécanique du solide ont été utilisées pour prendre en compte les grandes déformations locales du matériau (par la formulation corotationelle), et pour décrire les conditions de contact qui évoluent au cours de l'analyse dans le modèle à l'échelle des milieux continus (traitement des conditions de contact unilatérales et tangentielles par une forme de Lagrangien augmenté). L’application des modèles numériques a permis de contribuer à l’identification des phénomènes qui gouvernent la nanoindentation du nickel pur. Le comportement viscoplastique du nickel pur pendant nanoindentation a été identifié dans une étude expérimentale-numérique couplée, et l'effet cumulatif de la rugosité et du frottement sur la dispersion des résultats de la nanoindentation a été montré par une étude numérique (dont les résultats sont en accord avec des tendances expérimentales). Par ailleurs, l’utilisation de l’outil numérique pour une autre application à petites échelles, la manipulation des objets par contact, a contribué à la compréhension de la variation de l’adhésion électrostatique pendant micromanipulation. La déformation plastique des aspérités de surface sur le bras de manipulateur (en nickel pur) a été identifiée comme une source potentielle d’augmentation importante de l'adhésion pendant la micromanipulation, qui peut potentiellement causer des problèmes de relâche et de précision de positionnement, observés expérimentalement. Les résultats présentés dans cette thèse montrent que des simulations numériques basées sur la physique du problème traité peuvent expliquer des tendances expérimentales et contribuer à la compréhension et l'interprétation d'essais couramment utilisé pour la caractérisation aux petites échelles. Le travail réalisé dans cette thèse s’inscrit dans un projet de recherche appelé "mini-micro-nano" (mµn), financé par la Communauté Française de Belgique dans le cadre de "l'Action de Recherche Concertée", convention 04/09-310.

No description available.