A level-set approach to the computation of twinning and phase-transition dynamics

A computational method is proposed for the dynamics of solids capable of tw inning and phase transitions. In a two-dimensional, sharp-interface model o f twinning, the stored-energy function is a nonconvex potential with multip le wells. The evolution of twin interfaces is governed by held equations an d jump conditions of momentum balance, and by a kinetic relation expressing the interface velocity as a function of the local driving traction and int erfacial orientation. A regularized version of the model is constructed bas ed on the level-set method. A level-set function which changes signs across the interface is introduced, The evolution of this function is described b y a Hamilton-Jacobi equation, whose velocity coefficient is determined by t he kinetic relation. Jump conditions are thereby eliminated, allowing finit e-difference discretization. Numerical simulations exhibit complex evolutio n of the interface, including cusp formation, needle growth, spontaneous ti p splitting, and topological changes that result in microstructure refineme nt. The results capture experimentally observed phenomena in martensitic cr ystals. (C) 1999 Academic Press.