Lamination-based efficient treatment of weak discontinuities for non-conforming finite element meshes

TL;DR

This paper introduces a lamination-based method for efficiently handling weak discontinuities in non-conforming finite element meshes, simplifying complex interface modeling in 3D without requiring mesh conformity.

Contribution

It develops a novel laminated microstructure approach inspired by composite voxel techniques for non-conforming finite element treatment of interfaces.

Findings

Method outperforms simple alternatives in most cases

Applicable to elastic and elastic-plastic materials

Effective for complex 3D geometries

Abstract

When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the geometry is complex, in particular in 3D. In this work, we develop an efficient technique for a non-conforming finite-element treatment of weak discontinuities by using laminated microstructures. The approach is inspired by the so-called composite voxel technique that has been developed for FFT-based spectral solvers in computational homogenization. The idea behind the method is rather simple. Each finite element that is cut by an interface is treated as a simple laminate with the volume fraction of the phases and the lamination orientation determined in terms of the actual geometrical arrangement of the interface within the element. The approach is illustrated by several computational examples relevant to the micromechanics of heterogeneous materials. Elastic and elastic-plastic materials at small and finite strain are considered in the examples. The performance of the proposed method is compared to two alternative, simple methods showing that the new approach is in most cases superior to them while maintaining the simplicity.