Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag

Abstract

Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this work, we propose a model for the evolution of the grain boundary network with dynamic boundary conditions at the triple junctions, triple junctions drag, and with dynamic lattice misorientations. Using the energetic variational approach, we derive system of geometric differential equations to describe motion of such grain boundaries. Next, we relax curvature effect of the grain boundaries to isolate the effect of the dynamics of lattice misorientations and triple junctions drag, and we establish local well-posedness result for the considered model.