Virtual testing of composites: Imposing periodic boundary conditions on general finite element meshes

Predicting the effective thermo-mechanical response of heterogeneous materials such as composites, using virtual testing techniques, requires imposing periodic boundary conditions on geometric domains. However, classic methods of imposing periodic boundary conditions require identical finite element mesh constructions on corresponding regions of geometric domains. This type of mesh construction is infeasible for heterogeneous materials with complex architecture such as textile composites where arbitrary mesh constructions are commonplace. This paper discusses interpolation technique for imposing periodic boundary conditions to arbitrary finite element mesh constructions (i.e. identical or non-identical meshes on corresponding regions of geometric domains), for predicting the effective properties of complex heterogeneous materials, using a through-thickness angle interlock textile composite as a test case. Furthermore, it espouses the implementation of the proposed periodic boundary condition enforcement technique in commercial finite element solvers. Benchmark virtual tests on identical and non-identical meshes demonstrate the high fidelity of the proposed periodic boundary condition enforcement technique, in comparison to the conventional technique of imposing periodic boundary condition and experimental data.