Variationally consistent multi-scale modeling and homogenization of stressed grain growth Original Research Article

The macroscopic mechanical, thermal, and electromagnetic properties of materials are essentially determined by the microstructures of polycrystalline materials. This paper presents a multi-scale mathematical and computational framework for analyzing the global and local behavior of stressed grain growth. This is achieved by introducing an asymptotic expansion of field variables into the variational equation based on the principle of virtual power. The expanded variational equation gives rise to multi-scale Euler equations describing evolution processes at different scales, the scale-coupling relation, as well as the homogenized material properties. The multi-scale characteristics of grain boundary migration triggered by the multi-scale property of strain energy density jump across the grain boundaries are also discussed. A stressed grain growth example is analyzed to demonstrate multi-scale behavior of grain deformation and grain structure evolution under mechanical loading.