A study was made of the transient motion of a twin boundary in 2 dimensions. The twinning deformation was described as being an anti-plane shear deformation with discontinuous strains. The material was assumed to be compressible and hyper-elastic; with a stored energy function which consisted of multiple potential wells. The quasi steady-state evolution of a twinning step was studied, and the model included an anisotropic kinetic relationship which governed twin boundary motion in 2 dimensions under an applied stress. A self-similar solution for the motion of the twinning step was found for a specific initial shape. General solutions to the linearized evolution equation were established in the form of an infinite series for arbitrary initial shapes.

Self-Similar Evolution of a Twin Boundary in Anti-Plane Shear. H.Tsai: Journal of Engineering Mathematics, 2001, 40[2], 179-95