FEM/BEM formulation for multi-scale analysis of stretched plates

A multi-scale modelling for analysing the stretching problem of plates composed of heterogeneous materials is presented. The BEM (Boundary Element Method) is adopted to model the macro-continuum (represented by the plate) while the equilibrium problem at micro-scale (represented by the Representative Volume Element – RVE) is solved by a FEM (Finite Element Method) formulation that takes into account the Hill–Mandel Principle of Macro-Homogeneity. After solving the equilibrium problem of the RVE, the micro-to-macro transition is made by applying the volume averaging hypothesis of strain and stress tensors. Some numerical examples are then analysed to show that the proposed formulation is a suitable tool for the analysis of stretched of plates composed of heterogeneous materials. To define the microstructure, different RVEs composed of an elasto-plastic matrix with inclusions or voids are considered. Besides, a quadratic rate of asymptotic convergence of the Newton–Raphson scheme has been achieved during the iterative procedure.