A computationally effective 3D Boundary Element Method for polycrystalline micromechanics

An effective computational framework for homogenization and microcracking analysis of polycrystalline RVEs is presented. The method is based on a recently developed grain-boundary formulation for polycrystalline materials and several enhancements over the original technique are introduced to reduce the computational effort needed to model three-dimensional polycrystalline aggregates, which is highly desirable, especially in a multiscale perspective. First, a regularization scheme is used to remove pathological entities, usually responsible for unduly large mesh refinements, from Voronoi polycrystalline morphologies. Second, an improved meshing strategy is used, with an aim towards meshing robustness, a requirement often challenged by the inherent high statistical variability of Voronoi tessellations. Additionally, for homogenization purposes, the use of periodic non-prismatic polycrystalline RVEs is proposed as an alternative to the classical prismatic RVEs, generally employed in the literature. The proposed overall scheme promotes a remarkable reduction in the number of DoFs of the problem in hand, and thus outstanding savings in terms of computational time and memory storage. Furthermore, the smoother meshing strategy, combined with a Newton-Raphson method, enhances the convergence of the microcracking algorithm.