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Numerical and analytical aspects of the pinning of martensitic phase boundaries. (English) Zbl 1277.74060

Summary: We study the pinning and depinning behavior of interfaces immersed in a heterogeneous medium. For a continuum elasticicity model of the martensitic phase transformation, we numerically estimate the critical depinning stress of a phase boundary intersecting a non-transforming inclusion in the material. In the limit of a nearly flat phase boundary, the elastic energy of the phase boundary can be approximated by an elliptic operator of order 1. For such an approximation we study the depinning transition near the critical point. Finally, we prove the existence of a pinned solution for a parabolic model for the evolution of phase boundaries in a random environment.

MSC:

74N20 Dynamics of phase boundaries in solids
74S30 Other numerical methods in solid mechanics (MSC2010)
74E05 Inhomogeneity in solid mechanics
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