A micromechanical model for martensitic phase-transformations in shape-memory alloys based on energy-relaxation
T. Bartel, K. Hackl.
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 89, 792-809, (2009)
We develop a micromechanical model for single-crystalline materials undergoing diffusionless solid-to-solid phase transitions. It is based on the specification of laminated microstructures on the materials' microscale and hence is designed to approximate the rank-1-convex hull of the underlying energy-density for the phase-mixture. In order to capture the hysteretic behavior of such materials like shape-memory-alloys we also account for dissipation by means of evolution equations for the inelastic internal variables. In this context, we derive different evolution-laws from inelastic potentials via least-action principles. Several material-point computations emphasize the characteristics of the presented model. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Keyword(s): martensitic phase transformations, shape‐memory alloys, energy relaxation, quasi‐convexification
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