Micromechanical modelling of composite materials using the element-free galerkin approach

The microstructure of composite materials is often distinguished by the size, shape and distribution of the reinforcing constituents. Various analytical, semi-analytical and computational approaches have been developed to determine their effective properties and to study the evolution of damage in these materials. The finite element method (FEM) has emerged as the primary computational tool for micromechanical modelling, particularly for composites with complex microstructures or architecture. Nonetheless, the meshing of complex geometries may present difficulties. This is compounded by the challenge of modelling the propagation of cracks in heterogeneous materials. While the eXtended Finite Element Method (XFEM) mitigates the need for re-meshing, by incorporating enrichment functions in the finite element formulation to permit the propagation of cracks through an element, this chapter explores an alternative approach through the use of meshless methods. Such methods are based on a distribution of nodes, within a domain, which are not required to be interconnected. A number of these methods have been proposed over recent years and the element-free Galerkin (EFG) approach has been adopted in the work presented. This chapter introduces the basic concepts of the EFG method and is followed by an example of the use of the EFG method for constructing a representative volume element (RVE) of a composite material from which homogenised elastic properties are determined. A numerical strategy is subsequently proposed for propagating a crack through these composites, followed by the more complex case of propagating multiple interacting cracks, to yield insight into the formation of microscale damage. © 2018 Elsevier Ltd. All rights reserved.