A study was made of the growth, of a curved twin boundary, which involved a twinning step in 2 dimensions under an applied stress. The twinning deformation was described as being an anti-plane shear deformation with discontinuous strain. The material was assumed to be hyperelastic, with a non-convex multi-well stored-energy function. Twin boundary evolution was governed by an orientation-dependent kinetic relationship whose form was deduced from a dislocation model for the twin boundary. Steady-state evolution was precluded by the model. However, quasi-steady growth allowed for transient effects and for twin-boundary shape-changes that were slow when compared to the average growth speed. Twin-boundary evolution was then governed by a non-linear integro-differential equation. A particular analytical solution was found, and was shown to be globally asymptotically stable. It described the long-term behavior of twinning steps of arbitrary initial shape.

Quasi-Steady Growth of Twins under Stress. H.Tsai, P.Rosakis: Journal of the Mechanics and Physics of Solids, 2001, 49[2], 289-312