  In this thesis, a computational framework for microstructural modelling of
transverse behaviour of heterogeneous materials is presented. The context of
this research is part of the broad and active field of Computational
Micromechanics, which has emerged as an effective tool both to understand the
influence of complex microstructures on the macro-mechanical response of
engineering materials and to tailor-design innovative materials for specific
applications through a proper modification of their microstructure. The
computational framework presented in this thesis is based on the Virtual
Element Method (VEM), a recently developed numerical technique able to provide
robust numerical results even with highly-distorted meshes. The peculiar
features of VEM have been exploited to analyse two-dimensional representations
of heterogeneous materials microstructures. Ad-hoc polygonal multi-domain
meshing strategies have been developed and tested to exploit the discretisation
freedom that VEM allows. To further simplify the preprocessing stage of the
analysis and reduce the total computational cost, a novel hybrid formulation
for analysing multi-domain problems has been developed by combining the Virtual
Element Method with the well-known Boundary Element Method (BEM). The hybrid
approach has been used to study both composite material transverse behaviour in
presence of inclusions with complex geometries and damage and crack propagation
in the matrix phase. Numerical results are presented that demonstrate the
potential of the developed framework.
