Analysis of the constitutive response of heterogeneous materials by the boundary element method, considering different RVE microstructures

Numerical analyses to model the constitutive response of heterogeneous materials by a Boundary Element Formulation, developed in the context of a RVE-based multi-scale theory, are performed. In this case, the material microstructure is denoted as RVE (Representative Volume Element) and it is modelled by a zoned plate, where each sub-region represents the matrix or an inclusion. Besides, voids can also be defined inside the matrix to model the microstructure of porous materials. The dissipative phenomenon in the RVE is taken into account by considering an initial forces field which represents the dissipative forces. After imposing a constant strain vector to the RVE boundary, its homogenized constitutive response must be obtained. For that, the RVE equilibrium problem must be solved first, which is defined in terms of displacements fluctuations. In the numerical examples different microstructures are adopted to show how the RVE constitutive response changes when different volume fractions of inclusions or voids are considered. Besides, the constitutive re-sponse of a RVE where five inclusions are disposed aleatory is evaluated when different strains vectors are imposed to its boundary. The homogenized values for the stress vector and the constitutive tensor are compared to the formulation developed by the Finite Element Method in order to validate the Boundary Element Formulation.