A micromechanics-enhanced finite element formulation for modelling heterogeneous materials

Novak, J., Kaczmarczyk, L., Grassl, P., Zeman, J. and Pearce, C.J. (2012) A micromechanics-enhanced finite element formulation for modelling heterogeneous materials. Computer Methods in Applied Mechanics and Engineering, 201-4, 53 - 64. (doi:10.1016/j.cma.2011.09.003)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Grassl, Dr Peter and Novak, Dr Jan and Kaczmarczyk, Dr Lukasz and Pearce, Professor Christopher
Authors: Novak, J., Kaczmarczyk, L., Grassl, P., Zeman, J., and Pearce, C.J.
Subjects:T Technology > TA Engineering (General). Civil engineering (General)
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:14 September 2011

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