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In the present thesis, a computational framework for the analysis of thedeformation and damage phenomena occurring at the micro-scale ofpolycrystalline materials is presented.  Micro-mechanics studies are commonly performed using the Finite ElementMethod (FEM) for its versatility and robustness. However, finite elementformulations usually lead to an extremely high number of degrees of freedom ofthe considered micro-structures, thus making alternative formulations of greatengineering interest. Among the others, the Boundary Element Method (BEM)represents a viable alternative to FEM approaches as it allows to express theproblem in terms of boundary values only, thus reducing the total number ofdegrees of freedom.  The computational framework developed in this thesis is based on a non-linearmulti-domain BEM approach for generally anisotropic materials and is devoted tothe analysis of three-dimensional polycrystalline microstructures. Differenttheoretical and numerical aspects of the polycrystalline problem using theboundary element method are investigated: first, being the formulation based ona integral representation of the governing equations, a novel and more compactexpression of the integration kernels capable of representing the multi-fieldbehaviour of generally anisotropic materials is presented; second, the sourcesof the high computational cost of polycrystalline analyses are identified andsuitably treated by means of different strategies including an ad-hoc grainboundary meshing technique developed to tackle the large statisticalvariability of polycrystalline micro-morphologies; third, non-lineardeformation and failure mechanisms such as inter-granular and trans-granularcracking and generally anisotropic crystal plasticity are studied and thenumerical results presented throughout the thesis demonstrate the potential ofthe developed framework.

A computational framework for microstructural modelling of polycrystalline materials with damage and failure