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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i2.90
pages 291-304

Two-Dimensional Analysis of Shape Memory Alloys under Small Loadings

L. X. Wang
MCI, Faculty of Science and Engineering, University of Southern Denmark, Sonderborg, DK-6400, Denmark
Roderick V. N. Melnik
Center for Coupled Dynamics & Complex Systems, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, N2L 3C5, Canada

ABSTRACT

A mathematical model is constructed for modeling the behavior of shape memory alloy (SMA) patches in two dimensions. The effect of phase transformations is included into the model via a specific choice of the free energy functional valid for square-to-rectangular transformations. It is shown that the classical one-dimensional Falk dynamic model, applied to shape memory alloy rods, could be regarded as a special case of the formulated two-dimensional model. The model is analyzed numerically with the method of lines and a series of computational experiments for SMA materials is discussed, in detail, in order to compare the results of simulations to those obtained with conventional one-dimensional models.