| Abstract: |
| The coupling of phase transitions in shape memory alloys with plastic deformation induces intricate microstructure formation and gives rise to highly nonconvex energy functionals. In this talk, we study a class of variational models arising in single-slip finite crystal plasticity. In contrast to classical settings with a single elastic well, the elastic energy features two wells, leading to interactions between the slip system and the elastic phases under different compatibility constraints. To better understand the effective deformation behavior of these models, we analyze their relaxation, with focus on the quasiconvexification of the underlying extended-valued energy densities. After identifying the quasiconvex hull of the admissible deformation gradients, which shows that the effective states can vary within a range of volumetric responses, we derive bounds on the quasiconvex envelope from above and below. The upper bounds on the rank-one convex envelopes require careful constructions of suitable rank-one lines, while the established polyconvex lower bounds are generally smaller, but are shown to be optimal in a special case. |
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