A hybrid virtual–boundary element formulation for heterogeneous materials

In this work, a hybrid formulation based on the conjoined use of the recently developed virtual element method (VEM) and the boundary element method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the finite element method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary integral equations, employed as the original model of the represented physical problem. For several classes of problems, BEM offers some advantages over more popular techniques, namely the reduction of the dimensionality of the problem, with associated computational savings. In this study, the inherent advantages of VEM and BEM are simultaneously employed for the study of heterogeneous material microstructures. The method has been applied to i) the elastic analysis and ii) computational homogenization of fibre-reinforced composite materials and to iii) the analysis of composite unit cells exhibiting matrix isotropic damage. The discussed results show how the hybrid technique inherits the generality of VEM and the modelling simplification and accuracy of BEM, ensuring high accuracy and fast convergence and providing a versatile tool for the analysis of multiphase materials, also including non-linear behaviour such as material degradation. Further directions of research are identified and discussed after commenting on the presented results.