Probabilistic modeling of surface effects in nano-reinforced materials

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 a perturbed area at boundary between inclusion matrix phase. modeled as an interphase whose elastic properties randomly fluctuate from point to must be characterized probabilistic standpoint. In this study, we therefore address (i) stochastic modeling (ii) study relationship random model deterministic model. The aim twofold. First all, interested constructing for matrix-valued field, interphase. Then, used perform parametric apparent tensor associated microstructure. Simulations specifically characterize influence on material’s overall properties. When consistent physical view, computed by solving optimization problem involving effective medium.