two-scale three-dimensional boundary element framework fordegradation and failure in polycrystalline materials

A fully three-dimensional two-scale boundary element approach to degradation and failure inpolycrystalline materials is proposed. The formulation involves the engineering component level (macroscale)and the material grain scale (micro-scale). The damage-induced local softening at the macroscale ismodelled employing an initial stress approach. The microscopic degradation processes are explicitlymodelled by associating Representative Volume Elements (RVEs) to relevant points of the macrocontinuum and employing a three-dimensional grain-boundary formulation to simulate intergranulardegradation and failure in the microstructural Voronoi-type morphology through cohesive-frictional contactlaws. The scales coupling is achieved downscaling macro-strains as periodic boundary conditions for theRVE, while overall macro-stresses are obtained via volume averages of the micro-stress field. Thecomparison between effective macro-stresses for the damaged and undamaged RVE allows to define amacroscopic measure of material degradation. Some attention is devoted to avoiding pathological damagelocalization at the macro-scale. The multiscale processing algorithm is described and some preliminaryresults are illustrated.