Multi-scale modelling for bending analysis of heterogeneous plates by coupling BEM and FEM

A multi-scale modelling for analyzing the bending problem of plates composed of heterogeneous materials is presented. The macro-continuum is modelled by a non-linear formulation of the boundary element method (BEM) taking into account the consistent tangent operator (CTO). The micro-scale is represented by the RVE (representative volume element) being its equilibrium problem solved by a finite element formulation that takes into account the Hill-Mandel Principle of Macro-Homogeneity while the volume averaging hypothesis of the strain and stress tensors is used to make the micro-to-macro transition. Three different boundary conditions are imposed over the RVE: (i) linear displacements, (ii) periodic displacement fluctuation and (iii) uniform boundary tractions. The material behaviour is governed by the Von Mises elasto-plastic criterion although the proposed multi-scale model can be used with any other non-linear model. Numerical examples are presented to illustrate the main features and scope of the proposed formulation.