Contribution of FE and FFT-based methods to the determination of the effective elastic and conduction properties of composite media with flat inclusions and infinite contrast

Abstract

Homogenization theory is increasingly applied to coupled phenomena, i.e. when different physical processes have to be modeled in order to correctly describe a system. The reason is that this methodology provides the means to propose a consistent morphological description of the system irrespective of the different phenomena involved, which is deemed to be physically sound. Here, we perform numerical simulations of both mechanical and transport processes in a linear context, so as to identify the best homogenization scheme out of five classical ones. The goal is to eventually apply the result to cracked rocks, which present complex structures, but this study is restricted to the case of parallel disks in an otherwise isotropic matrix. Since cracks in rocks present a vanishing stiffness but an infinite conductivity with respect to the rock, both types of contrast will be considered, and the reverse cases as well (infinite stiffness and vanishing conductivity) for the sake of completeness.After detailing the motivations behind this work, the theoretical background necessary to derive all the analytical estimates is laid down. The derivations given are somewhat improved over previously published ones, and the framework is extended to deal with vanishing as well as infinite contrast. The methodology is explained for the 3D numerical simulations, and the results are presented and discussed. Two different numerical strategies have been used: an FEM software and an FFT-based code. This allows to lessen potential biases of a particular method, and increases the credibility of the results. All in all, the differential scheme is identified as the best fit, which confirms the results of previous studies, but this time in several different cases.