Equilibrium conditions at corners and edges of an interface in a multiphase solid

In various situations such as coherent precipitation, martensitic transformation, recrystallization, and grain growth the kinetics of phase boundaries play a crucial role in determining the microstructure and the resulting macroscopic properties. By performing a variational calculation in a two dimensional setting, we find the equilibrium conditions at corners, where two interfaces meet, and at edges, where an interface meets the boundary of a finite body. We allow for possible singularities in the bulk stress at corners and edges. The general case considers elastic energy for the bulk and anisotropic energies for the surfaces. Special cases treated are: (i) constant bulk energy or purely surface case; (ii) purely elastic case or zero surface energy; and (iii) constant surface energy.