  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.
