Enforcing periodic boundary conditions on general finite element discretisations of heterogeneous materials

Abstract

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 techniques for imposing periodic boundary conditions on general finite element mesh constructions for predicting the effective elastic properties of a variety of heterogeneous materials. Benchmark virtual tests on identical and non-identical meshes demonstrate the high fidelity of the proposed periodic boundary conditions enforcement technique, in comparison to a conventional technique of imposing periodic boundary conditions and experimental data.

Whitney face elements for the analysis of periodic structures using arbitrary meshes

“…This last is carried out by using either the Lagrange interpolation formulation or the cubic spline interpolation formulation and it has been applied for computing the mechanical properties. In [17], a technique has been presented for characterising the mechanical response of heterogeneous materials. The periodic boundary conditions are enforced by interpolating the displacement field on boundary utilising two piecewise interpolation techniques: (i) cubic Hermite interpolation and (ii) linear triangulation interpolation.…”