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Proceedings Paper

Computations of twinning in shape-memory materials
Author(s): Charles R. Collins
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Paper 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.

Paper Details

Date Published: 22 July 1993
PDF: 8 pages
Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); doi: 10.1117/12.148408
Show Author Affiliations
Charles R. Collins, Univ. of Michigan (United States)

Published in SPIE Proceedings Vol. 1919:
Smart Structures and Materials 1993: Mathematics in Smart Structures
H. Thomas Banks, Editor(s)

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