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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 3647470, 19 pages
Research Article

Effect of Aspect Ratio and Boundary Conditions in Modeling Shape Memory Alloy Nanostructures with 3D Coupled Dynamic Phase-Field Theories

1Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, Canada M5S 3G8
2Department of Applied Mathematics, University of A Coruña, Campus de Elvina, s/n, 15192 A Coruña, Spain
3MS2Discovery Interdisciplinary Research Institute, M2NeT Laboratory, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5

Received 20 June 2016; Revised 10 September 2016; Accepted 19 September 2016

Academic Editor: Mohsen Asle Zaeem

Copyright © 2016 R. Dhote et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The behavior of shape memory alloy (SMA) nanostructures is influenced by strain rate and temperature evolution during dynamic loading. The coupling between temperature, strain, and strain rate is essential to capture inherent thermomechanical behavior in SMAs. In this paper, we propose a new 3D phase-field model that accounts for two-way coupling between mechanical and thermal physics. We use the strain-based Ginzburg-Landau potential for cubic-to-tetragonal phase transformations. The variational formulation of the developed model is implemented in the isogeometric analysis framework to overcome numerical challenges. We have observed a complete disappearance of the out-of-plane martensitic variant in a very high aspect ratio SMA domain as well as the presence of three variants in equal portions in a low aspect ratio SMA domain. The dependence of different boundary conditions on the microstructure morphology has been examined energetically. The tensile tests on rectangular prism nanowires, using the displacement based loading, demonstrate the shape memory effect and pseudoelastic behavior. We have also observed that higher strain rates, as well as the lower aspect ratio domains, resulting in high yield stress and phase transformations occur at higher stress during dynamic axial loading.