A boundary element formulation to perform elastic analysis of heterogeneous microstructures

Abstract

A BEM formulation to perform elastic analysis of heterogeneous microstructures is proposed in the context of multi-scale analysis. The microstructure, also denoted as RVE (Representative Volume Element), is modeled as a zoned plate where voids or inclusions can be considered inside a matrix. Thus, each sub-region represents either the matrix or an inclusion, where different values of Poisson's ratio and Young's modulus can be defined. The RVE equilibrium equation is solved in terms of displacement fluctuations according to the formulation proposed in de Souza Neto and Feijóo (2006). Only elastic behavior is considered for matrix and inclusions, although the proposed model can be extended to consider dissipative phenomena. To make the micro-to-macro transition necessary in a multi-scale analysis, the homogenized values for stress and constitutive tensor have to be computed adopting homogenization techniques. Some numerical examples of heterogeneous microstructures are presented and compared to a FEM model to show the accuracy of the proposed model.