Measure of combined effects of morphological parameters of inclusions within composite materials via stochastic homogenization to determine effective mechanical properties

In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from these methods to analyze the influence of the morphology on the effective mechanical properties of the samples. More precisely, we study the dependence of main mechanical characteristics of a composite medium on various parameters of the mixture of inclusions composed of spheres and cylinders. On top of that we introduce various imperfections to inclusions and observe the evolution of effective properties related to that. The main computational approach used throughout the work is the FFT-based homogenization technique, validated however by comparison with the direct finite elements method. We give details on the features of the method and the validation campaign as well. Keywords: Composite materials, Cylindrical and spherical reinforcements, Mechanical properties, Stochastic homogenization.Comment: 23 pages, updated figures, version accepted to Composite Structures 201

Résolution du problème limite des coques élastiques en flexion dans le cas d’un paraboloïde hyperbolique

International audienc

On Geometrical Rigidity of Surfaces.

International audienc

Some solutions to the asymptotic bending problem of non-inhibited shells.

We study the asymptotic limit bending problem of thin linearly elastic shells as the thickness goes to zero. Such asymptotic bending problem makes sense whenever bendings are admissible. We present two alternate expressions of the change of curvature tensor giving new formulations for the asymptotic bending problem. In some case of cylinders and hyperbolic surfaces, we are able present solutions, eventually analytic. Such solutions can constitute tests for the membrane locking

A Finite Difference Element Method for thin elastic Shells

We present, in this paper, a four nodes quadrangular shell element (FDEM4) based on a Finite Difference Element Method procedure that we introduce. Its stability and robustness with respect to shear locking and membrane locking problems is discussed. Numerical tests including inhibited and non-inhibited cases of thin linear shells are presented and compared with widely used DKT and MITC4 elements

A Fictitious Domain Method for Numerical Homogenization

Numerical Homogenization gives numerical approximations of the effective properties of a composite material. In the case of periodic composite, multi-scale modeling allows to consider only a Representative Volume Element (RVE). In this paper, we propose an original finite element method based on fictitious domain principle, in which the RVE is represented by a structured mesh and the inclusions are represented by independent and non matching meshes. The integral computations on inclusions meshes are substituted into the structured mesh of the RVE, with the help of a connection matrix

On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

International audienc

Computation of effective electrical conductivity of composite materials: a novel approach based on analysis of graphs

International audienceIn this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called 'stochastic homogenization'. In this approach, the classical deterministic homogenization techniques and procedures are used to compute the macroscopic parameters of a composite starting from its microscopic properties. The stochastic part is due to averaging over some series of samples, and the fact that these samples fit into the concept of RVE (Representative Volume Element) in order to reduce the variance effect. In this article, we present a novel method for computation of effective electric properties of composites-it is based on the analysis of the connectivity graph (and the respective adjacency matrix) for each sample of a composite material. We describe how this matrix is constructed in order to take into account complex microscopic geometry. We also explain what we mean by homogenization procedure for electrical conductivity, and how the constructed matrix is related to the problem. The developed method is applied to a test study of the influence of micromorphology of composites materials on their conductivity

RVE GENERATION BASED ON MOLECULAR DYNAMICS - APPLICATIONS

International audienc