Probabilistic modeling of surface effects in nano-reinforced materials

Abstract

This work is concerned with multiscale analysis of nano-reinforced heterogeneous materials. Such materials exhibit surface effects that are typically taken into account through interface models in mean-field homogenization theories. However, both experiments and numerical simulations demonstrate the existence of a perturbed area at the boundary between the inclusion and the matrix phase. This area is modeled as an interphase whose elastic properties randomly fluctuate from point to point and must be characterized from a probabilistic standpoint. In this study, we therefore address (i) the stochastic modeling of the interphase and (ii) the study of the relationship between the random interphase model and a deterministic interface model. The aim of this work is twofold. First of all, we are interested in constructing a probabilistic model for the matrix-valued random field, modeling the elastic properties of the interphase. Then, this model is used to perform a parametric study for the apparent tensor associated with the microstructure. Simulations are specifically used to characterize the influence of both the random interphase and interface models on the material’s overall properties. When the interface model is consistent from a physical point of view, the associated elastic surface properties are computed by solving an optimization problem involving the effective properties of the random medium.