A micromechanics-enhanced finite element formulation for modelling heterogeneous materials

TL;DR

This paper introduces a micromechanics-enhanced finite element method that efficiently models heterogeneous composite materials by incorporating analytical solutions for inclusions, avoiding explicit heterogeneity resolution and additional degrees of freedom.

Contribution

It develops a finite element formulation that integrates micromechanical solutions to accurately simulate heterogeneous materials without mesh refinement.

Findings

Accurately predicts mechanical behavior of composites

No additional degrees of freedom needed

Demonstrated with numerical examples

Abstract

In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite element formulation that accurately captures the mechanical behaviour of heterogeneous materials in a computationally efficient manner. The strategy exploits analytical solutions derived by Eshelby for ellipsoidal inclusions in order to determine the mechanical perturbation fields as a result of the underlying heterogeneities. Approximation functions for these perturbation fields are then incorporated into a finite element formulation to augment those of the macroscopic fields. A significant feature of this approach is that the finite element mesh does not explicitly resolve the heterogeneities and that no additional degrees of freedom are introduced. In this paper, hybrid-Trefftz stress finite elements are utilised and performance of the proposed formulation is demonstrated with numerical examples. The method is restricted here to elastic particulate composites with ellipsoidal inclusions but it has been designed to be extensible to a wider class of materials comprising arbitrary shaped inclusions.