On the deformation dependency of the diffusion flux in solids at large deformations

Abstract

In material modeling, when dealing with diffusion at large deformations, there are usually two different variants for the diffusion flux: an isotropic law in the current placement and an isotropic law in the reference placement. The first one causes diffusion behavior, which is independent from the initial shape of the body, i.e., it causes a deformation-independent behavior. The second one relates the diffusion solely to the initial shape of the body, which results in a deformation-dependent behavior in the current state. In most of the works in the literature, one of these two possible formulations is chosen arbitrarily. While the modern description of diffusion at large deformations mostly evolved in the last two decades, to our best knowledge, there are no works which discuss or motivate the choice for one of these two versions really in detail. In the present article, we approach the motivation for the choice of the two different types of diffusion flux formulations. We illustrate their characteristics and discuss their application under different circumstances. It is important to note that the deformation dependency which arises from choosing the isotropic reference placement formulation is quite specific and strongly differs from the actual behavior of many materials. We investigate such a case with a more individual deformation dependency based on a very simple artificial microstructure. We determine the properties on the macroscale using representative volume elements within numerical homogenization.