Non-smooth contact dynamics approach of cohesive materials

International audienceThe main features of the non-smooth contact dynamics (NSCD) method—the dynamical equation, the Signorini relation as a non-smooth modelling of unilateral contact, and the frictional Coulomb's law, treated with fully implicit algorithms— are briefly presented in this paper. By mere changes of variables, it appears that a large class of interface problems, including cohesive interface problems, may be solved using Signorini, Coulomb and standard NSCD algorithms. Emphasis is put on contact between deformable bodies. Examples illustrating numerical simulation are given for fibre-reinforced materials and for buildings made of blocks

Ductile damage of porous materials with two populations of voids

International audienceThis note presents an upper bound and an estimate for the yield yield function of a material with a rigid ideally plastic matrix and two scale cavities. The results are compared to numerical simulations. The laws of evolution of the two porosities are determined

Porous materials with two populations of voids under internal pressure: II. Growth and coalescence of voids

International audienceThis study is devoted to the mechanical behavior of polycrystalline materials with two populations of voids, small spherical voids located inside the grains and larger spheroidal voids located at the grain boundaries. In part I of the work, instantaneous effective stress-strain relations were derived for fixed microstructure. In this second part, the evolution of the microstructure is addressed. Differential equations governing the evolution of the microstructural parameters in terms of the applied loading are derived and their integration in time is discussed. Void growth results in a global softening of the stress-strain response of the material. A simple model for the prediction of void coalescence is proposed which can serve to predict the overall ductility of polycrystalline porous materials under the combined action of thermal dilatation and internal pressure in the voids

Computational non-smooth fracture dynamics in nonlinear and heterogeneous materials. Application to fracture of hydrided Zircaloy

This paper presents a new computational method and the associated software dedicated to the study of the dynamic fracture of nonlinear and heterogeneous materials. This method is based on the concept of Frictional Cohesive Zone Model in the framework of Non-Smooth Contact Dynamics. The associated numerical platform, composed of three object-oriented libraries, allows to simulate, in three dimensional finite deformations, the dynamic fracture of both multiphase and functionally graded materials from crack initiation to post-fracture behavior. The ability of this software, developed by the French ’Institut de Radioprotection et de Sûreté Nucléaire’ (IRSN) in the frame of its research program on nuclear fuel safety, is illustrated on the fracture of hydrided Zircaloy-4, constituting nuclear cladding tubes at high burnup, during a reactivity initiated accident (RIA). The macroscopic behavior of this heterogeneous material is deduced as an averaged energy release rate depending on the volume fraction of hydride phase

Chemo-poro-mechanical modeling of cementitious materials (diffusion-precipitation-cracking)

International audienceThe present work focuses on the impact of the chemical degradations of cementitious materials such as Delayed Ettringite Formation (DEF) on the overall material properties. DEF is an endogenous pathology due to the crystallization of ettringite within voids and cracks. The crystallization pressure in the porous cement paste induces swelling and cracking by differential expansion. The study aims to characterize the evolution of effective material properties (diffusion coefficient, apparent tenacity) with respect to DEF. A non-linear chemo-mechanical modeling is proposed where the entire diffusion-precipitation-pressurization-crack process is solved in a staggered approach. The diffusion-precipitation mechanism is translated by a rough chemical model. The resulting local volume fraction of ettringite is estimated by a finer micro-mechanical-based model using the effective elastic properties of the cement paste. The crack initiation and propagation is estimated with a dedicated cohesive zone model including pressure effect. Some applications of the model are presented

Determination of the size of the representative volume element for random quasi-brittle composites

International audienceA representative volume element (RVE) is related to the domain size of a microstructure providing a ''good" statistical representation of typical material properties. The size of an RVE for the class of quasi-brittle random heterogeneous materials under dynamic loading is one of the major questions to be answered in this paper. A new statistical strategy is thus proposed for the RVE size determination. The microstructure illustrating the methodology of the RVE size determination is a metal matrix composite with randomly distributed aligned brittle inclusions: the hydrided Zircaloy constituting nuclear clad-dings. For a given volume fraction of inclusions, the periodic RVE size is found in the case of overall elastic properties and of overall fracture energy. In the latter case, the term ''representative" is discussed since the fracture tends to localize. A correlation factor between the ''elastic" RVE and the ''fracture" RVE is discussed

Fracture of heterogeneous graded materials : from microstructure to structure

10.1016/j.engfracmech.2007.07.017This paper presents a new computational approach dedicated to the fracture of nonlinear heterogeneous materials. This approach extends the standard periodic homogenization problem to a two field cohesive-volumetric finite element scheme. This two field finite element formulation is written as a generalization Non-Smooth Contact Dynamics framework involving Frictional Cohesive Zone Models. The associated numerical platform allows to simulate, at finite strain, the fracture of nonlinear composites from crack initiation to post-fracture behavior. The ability of this computational approach is illustrated by the fracture of the hydrided Zircaloy under transient loading

Effective flow surface of porous materials with two populations of voids under internal pressure: II. full-field simulations

International audienceThis study is devoted to the effective plastic flow surface of a bi-porous material saturated by a fluid. Highly irradiated uranium dioxide is a typical example of such a material. In part I of this study, a GTN-type approximation of the effective plastic flow surface has been derived. In this second part, the predictions of this new model are compared with full-field numerical simulations performed with a numerical method based on Fast Fourier Transforms. This method is successfully applied to voided materials with a Gurson matrix where the voids are subjected to internal pressure. Different microstructures containing a large number of spherical or ellipsoidal voids are investigated. The deviation from isotropy of their mechanical response is measured by a new criterion

Plan d'expériences numériques adaptatifs pour les études mécaniques

La prise en compte des incertitudes fait aujourd’hui partie intégrante des analyses en mécanique des matériaux et des structures : variabilité des agencements microstructuraux, connaissance imprécise des propriétés matériaux, volumes élémentaires représentatifs, statistiques de défauts, écarts aux prescriptions géométriques des structures, évolutions temporelles non maîtrisables des chargements, etc. La propagation de ces connaissances incertaines dans les logiciels de calcul complexes requiert en général un nombre important de simulations numériques vite rédhibitoire en pratique. Afin de réduire ce coût de calcul, des approches statistiques basées sur la théorie des plans d’expériences peuvent être utilisées. Une stratégie classique de plan d’expérience consiste à assurer une bonne couverture de l’espace de variation des entrées. Cependant, l’uniformité d’une telle répartition n’est pas optimale quand on s’intéresse à des caractéristiques locales de la réponse des structures : fortes variations des comportements apparents en fonction des paramètres d’entrées (gradients), optimisation topologique ou matérielle, etc. Ces connaissances précises nécessitent de concentrer les simulations dans des régions spécifiques plutôt que d’explorer l’ensemble de l’espace de variation. Ce travail est donc dédié au développement de techniques de planification adaptatives pour raffiner localement l’échantillonnage autour d’une zone d’intérêt. Une nouvelle méthode, basée sur un couplage d’interpolation par Krigeage et d’optimisation d’une fonction coût (une variante du critère d’Expected Improvement) intégrant l’objectif visé, est proposée. La pertinence et l’efficacité de cette méthode ont été soulignées dans le cadre d’une étude de compacité maximale pour un empilement de sphères polydisperses. Pour une situation bi-disperse, le problème consiste en la recherche d’une ligne de crête en fonction de l’étalement granulométrique et de la fraction volumique de chaque classe. La méthodologie générale proposée, utilisée ici avec le logiciel LMGC90, permet de retrouver à moindre coût des résultats de la littérature obtenus par des plans d’expérience uniformes et intensifs

Micro-rheology of dense particulate flows: Application to immersed avalanches

International audienceWe rely here on a non-smooth contact dynamics (NSCD) approach to treat particle collisions in a direct numerical simulation of a dense particulate flow. Interactions between particles are considered by a non-smooth formulation of particle dynamics at the microscopic scale, which enables one to straight forwardly implement complex contactlaws. The hydrodynamic coupling is achieved by a distributed Lagrange multiplier/fictitious domain (DLM/FD) method . As a preliminary step, the relevance of our NSCD-DLM/FD method is assessed by comparing results of 2D sedimentation simulations with those obtained with a usual molecular dynamics collision model. Then, we use it to investigate how a fully immersed granular packing collapses depending on its initial particle volume fraction, providing clues on the micro-rheology of dense particulate flows