A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales

AbstractIn this work, the question of homogenizing linear elastic, heterogeneous materials with periodic microstructures in the case of non-separated scales is addressed. A framework if proposed, where the notion of mesoscopic strain and stress fields are defined by appropriate integral operators which act as low-pass filters on the fine scale fluctuations. The present theory extends the classical linear homogenization by substituting averaging operators by integral operators, and localization tensors by nonlocal operators involving appropriate Green functions. As a result, the obtained constitutive relationship at the mesoscale appears to be nonlocal. Compared to nonlocal elastic models introduced from a phenomenological point of view, the nonlocal behavior has been fully derived from the study of the microstructure. A discrete version of the theory is presented, where the mesoscopic strain field is approximated as a linear combination of basis functions. It allows computing the mesoscopic nonlocal operator by means of a finite number of transformation tensors, which can be computed numerically on the unit cell

Topology optimization of particle-matrix composites for optimal fracture resistance taking into account interfacial damage

AcceptedInternational audienceThis paper presents a topology optimization framework for optimizing the fracture resistance of two-phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bi-directional evolutionary structural optimization (BESO) method. The sensitivity formulation accounts for the whole fracturing process involving cracks nucleation, propagation and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended BESO method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process

A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure

International audienceIn this work, crack initiation and propagation in 2D and 3D highly heterogeneous materials models, such as those obtained by micro-CT imagery of cementitious materials, is investigated for the first time by means of the phase field method. A shifted strain split operator algorithm is proposed to handle unilateral contact within cracks in a very efficient manner. The various advantages of the phase field method for voxel-based models are discussed. More specifically, we show that the resolution related to the initial image and thus to meshes for discretizing the same microstructure does not significantly affect the simulated crack path

Topology optimization of periodic lattice structures taking into account strain gradient

International audienceWe present a topology optimization for lattice structures in the case of non-separated scales, i.e. when the characteristic dimensions of the periodic unit cells in the lattice are not much smaller than the dimensions of the whole structure. The present method uses a coarse mesh corresponding to a homogenized medium taking into strain gradient through a non-local numerical homogenization method. Then, the topological optimization procedure only uses the values at the nodes of the coarse mesh, reducing drastically the computational times. We show that taking into account the strain gradient within the topological optimization procedure brings significant increase in the resulting stiffness of the optimized lattice structure when scales are not separated, as compared to using a homogenized model based on the scale separation assumption

On the choice of parameters in the phase field method for simulating crack initiation with experimental validation

International audienceThe phase field method is a versatile simulation framework for studying initiation and propagation of complex crack networks without dependence to the finite element mesh. In this paper, we discuss the influence of parameters in the method and provide experimental validations of crack initiation and propagation in plaster specimens. More specifically, we show by theoretical and experimental analyses that the regularization length should be interpreted as a material parameter, and identified experimentally as it. Qualitative and quantitative comparisons between numerical predictions and experimental data are provided. We show that the phase field method can predict accurately crack initiation and propagation in plaster specimens in compression with respect to experiments, when the material parameters, including the characteristic length are identified by other simple experimental tests

Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved

Modelling of interfacial crack propagation in strongly heterogeneous materials by using phase field method

Phase field model has been proved to be a useful tool to study the fracture behaviors in heterogeneous materials. This method is able to model complex, multiple crack fronts, and branching in both 2D/3D without ad-hoc numerical treatments. In this study, a new interfacial cracking model in the phase field framework is proposed. The effects of both stiff and soft interphases on the fracture response of composite materials are considered. A dimensional-reduced model based on a rigorous asymptotic analysis is adapted to derive the null thickness imperfect interface models from an original configuration containing thin interphase. The idea of mixing the bulk and interfacial energy within the phase field framework is then used to describe the material degradation both on the interface and in bulk. Moreover, in order to ensure the physical crack propagation patterns, a unilateral contact condition is also proposed for the case of spring imperfect interface. The complex cracking phenomena on interfaces such as initiation, delamination, coalescence, deflection, as well as the competition between the interface and bulk cracking are successfully predicted by the present method. Concerning the numerical aspect, the one-pass staggered algorithm is adapted, providing an extremely robust approach to study interfacial cracking phenomena in a broad class of heterogeneous materials

Nouvelles approches basées sur la réduction de modèle pour le calcul multi-échelles des matériaux hyperélastiques en grandes déformations

Dans cette étude, nous présentons une méthode multi-échelle pour l'homogénéisation des matériaux hétérogènes, hyperélastiques, en grandes déformations. Une méthode d'éléments finis multi niveaux est utilisée en tandem avec une méthode de réduction de modèle de type POD pour alléger les coûts liés aux nombreux problèmes non linéaires qu'il est nécessaire de résoudre aux points de Gauss. Une extension de cette technique en vue de traiter les instabilités au niveau microscopique est proposée, par le biais d'une technique de perturbation avec continuation. Dans les différentes approches, chaque problème non linéaire associé à l'échelle microscopique est remplacé par un problème de petite taille (quelques dizaines de degrés de liberté). Des gains significatifs en temps de calculs liés à l'assemblage et la décomposition des matrices tangentes sont obtenus, ainsi qu'un gain de place mémoire lié à la réduction de la taille de la base décrivant l'histoire des différentes domaines micro