A computational method was proposed for treating the dynamics of solids that were capable of twinning and undergoing phase transitions. In a 2-dimensional sharp-interface model of twinning, the stored-energy function was a non-convex potential with multiple wells. The evolution of twin interfaces was governed by field equations and jump conditions of momentum balance, and by a kinetic relationship which expressed the interface velocity as a function of the local driving traction and interfacial orientation. A version of this model was constructed which was based upon the level-set method. A level-set function which changed sign across the interface was introduced. The evolution of this function was described by a Hamilton-Jacobi equation whose velocity coefficient was determined by the kinetic relationship. Jump conditions were thus eliminated; permitting finite-difference discretization. Numerical simulations revealed a complex evolution of the interface: including cusp formation, needle growth, spontaneous tip-splitting and topological changes that resulted in microstructural refinement. The results reproduced experimentally observed-phenomena in martensitic crystals.

A Level-Set Approach to the Computation of Twinning and Phase-Transition Dynamics. T.Y.Hou, P.Rosakis, P.LeFloch: Journal of Computational Physics, 1999, 150[2], 302-31