An integral framework for computational thermo-elastic homogenization of polycrystalline materials

A grain scale framework for thermo-elastic analysis and computational homogenization of polycrystalline materials is proposed. The morphology of crystal aggregates is represented employing Voronoi tessellations, which retain the main statistical features of polycrystalline materials. The behaviour of the individual grains is modelled starting from an integral representation for anisotropic thermo-elasticity, which is numerically addressed through a dual reciprocity boundary element method. The integrity of the aggregate is enforced through suitable intergranular thermo-elastic continuity conditions. By virtue of the features of the underlying formulation, the polycrystalline thermo-elastic problem is expressed in terms of grain boundary variables only, thus simplifying the subsequent task of meshing and reducing the overall computational cost of the analysis, ultimately providing an appealing tool for multiscale applications. The framework has been tailored for computational thermo-elastic homogenization of polycrystalline materials and it has been applied to the statistical computational homogenization of SiC and Al2O3 polycrystals, with accurate results confirming its robustness and effectiveness. The extension of the proposed framework to multiscale modelling of materials failure in thermally active environments is eventually discussed.