Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme

The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well-known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the problem, resulting in substantial simplification of the pre-processing stage and in the reduction of the computational effort, without jeopardising the solution accuracy. In this contribution, we explore the possibility of a coupling VEM and BEM for computational homogenisation of heterogeneous materials with complex microstructures. The test morphologies consist of unit cells with irregularly shaped inclusions, representative e.g. of a fibre-reinforced polymer composite. The BEM is used to model the inclusions, while the VEM is used to model the surrounding matrix material. Benchmark finite element solutions are used to validate the analysis results.