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Quasi-steady growth of twins under stress. (English) Zbl 1102.74325
The evolution of twin boundaries plays an important role in shape-memory-alloys. In this paper the authors investigate the growth of a curved twin boundary under applied stress. To enforce a unique representation the usual field equations and jump conditions have to be complemented by a constitutive equation for the twin boundary motion. Starting from dislocation kinetics combined with geometrical aspects of interface motion, the authors derive a class of kinetic relations with explicit orientation dependence.
Assuming that transient effects and twin boundary shape changes are slow compared to the average growth speed they obtain a nonlinear integro-differential equation to describe quasi-steady growth. In the special case of low applied stress the authors show that the kinetic relation completely determines the evolution of arbitrary initially steplike boundary curves. The investigation of long-time behaviour yields a complete flattening.

MSC:
74N20 Dynamics of phase boundaries in solids
74B20 Nonlinear elasticity
74M25 Micromechanics of solids
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