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

Abstract

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.

On the Influence of the Inclusions’ Morphology on the Accuracy of the Prediction of Reinforced Composites Mechanical Behaviour

“…An example of a sample with a mixture of nonintersecting spherical and cylindrical inclusions is presented on the figure 1a. Because mean-field approaches usually describe inclusions shape by the means of ellipsoids, we introduced imperfections (see [2] for more details) on the cylinder inclusions without spoiling the efficiency of the generation algorithm, in order to obtain ellipsoidal inclusions instead of cylinder. Once the RVE are generated, one seeks to find out the effective mechanical properties.…”

“…The transition between the local coordinate system Ri of the inclusion and the RVE system RI is made by these three Euler angles in the Bunge convention [8] where the transformation matrix is given by the following equation (1). This matrix is applied, for a given rank four tensor K, as showed in equation (2). cos sin cos sin sin sin cos cos cos cos sin sin cos sin cos cos sin sin sin cos cos sin sin cos cos sin sin cos cos , , m 2 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 (1)…”

“…The full-field approach used in this paper is the Fast Fourier Transform-based (FFTb) homogenization technique [2] where an iterative scheme is used for computing effective properties of each given RVE (Representative Volume Element). One of the main advantages of this approach is its low time and memory consumption in comparison for example with finite elements methods.…”

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

“…We have performed a detailed study of the effective elastic properties of composite materials in [3] and it included also some tests to choose the size of the RVE. Let us just mention here that if the volume fraction and the proportion of each type of inclusions are fixed, the choice of the size of the RVE is governed by the number of inclusions.…”

“…In what follows, we will see that it is very important to carefully choose suitable methods, and this choice is greatly influenced by the problem one is solving or by a property one is studying, and also by availability and type of the input data. In our previous papers we have observed for example, that the methods based on Fast Fourier Transform proposed initially in [1,2] for 2D problems, are perfectly suitable for studying elastic properties in 3D ( [3]), but they have to be modified to be applied to thermal phenomena ( [4,5]). It became clear from the previous studies ( [6]) that they are practically not efficient to estimate electrical conductivity, which is the main motivation for 1 Similar logic goes far beyond the subject of composite materials: one can for example recall the Nobel Prize 2013 in chemistry, that was given more or less for advances in computer simulations.…”