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 twinning and phase transitions. In a two-dimensional, sharp-interface model of twinning, the stored-energy function is a nonconvex potential with multiple wells. The evolution of twin interfaces is governed by field equations and jump conditions of momentum balance, and by a kinetic relation expressing the interface velocity as a function of the local driving traction and interfacial orientation. A regularized version of the model is constructed based on the level-set method. A level-set function which changes signs across the interface is introduced. The evolution of this function is described by a Hamilton?Jacobi equation, whose velocity coefficient is determined by the kinetic relation. Jump conditions are thereby eliminated, allowing finite-difference discretization. Numerical simulations exhibit complex evolution of the interface, including cusp formation, needle growth, spontaneous tip splitting, and topological changes that result in microstructure refinement. The results capture experimentally observed phenomena in martensitic crystals.