Computations of twinning in shape-memory materials

Charles R. Collins

doi:10.1117/12.148408

22 July 1993 Computations of twinning in shape-memory materials

Charles R. Collins

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148408
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

Abstract

One feature of shape memory alloys and other smart materials is the formation of fine-scale arrangements (microstructures) as a response to external stimuli. In shape memory materials there is twinning, where the material forms narrow bands in its interior, where in each band the material has a uniform orientation, but in adjacent bands it takes on different but symmetry-related orientations. In this paper, we discuss two different approaches to computing twinned configurations. The first is a variation on the conjugate gradient method applied to computing approximate minimizers of a model of the material energy for a shape memorsy material in the martensitic phase. This energy functional is not convex so special considerations are needed to assure that the method does not get stuck in the many local minima. The second method uses a multigrid based approach, averaging the approximate minimizers to include a probability distribution of the various orientations within the solution, i.e., it uses a Young measure to compute the minimizer.

Citation Download Citation

Charles R. Collins "Computations of twinning in shape-memory materials", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148408

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