Quasi-steady growth of twins under stress

We study the growth of a curved twin boundary involving a twinning step in two dimensions under applied stress, The twinning deformation is described as an anti-plane shear deformation with discontinuous strains. The material is assumed to be hyperelastic with a nonconvex, multiwell stored-energy fu nction. Twin boundary evolution is governed by an orientation-dependent kin etic relation whose form is derived from a dislocation model of the twin bo undary. Since steady-state evolution is precluded by this model, we study q uasi-steady growth, which allows for transient effects and twin boundary sh ape changes that are slow compared to the average growth speed. Twin bounda ry evolution is then governed by a nonlinear integro-differential equation. A particular analytical solution is found and shown to be globally asympto tically stable. It describes the long-time behavior of twinning steps with arbitrary initial shape. (C) 2001 Elsevier Science Ltd. All rights reserved .