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A Three-Dimensional Model of Shape Memory Alloys under Coupled Transformation and Plastic Deformation

B. Chen1,2, X. Peng1,2,3, X. Chen1,2, J. Wang4, H. Wang4, N. Hu1,5,6

Department of Engineering Mechanics, Chongqing University, Chongqing, China
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
Corresponding author: X. Peng, Email address:
Academy of Engineering Physics, Mianyang, Sichuan, 621900, China
Department of Mechanical Engineering, Chiba University, Chiba, Japan
Corresponding author: Ning Hu, E-mail address:

Computers, Materials & Continua 2012, 30(2), 145-176.


A three-dimensional phenomenological model for coupled transformation and plastic behavior of shape memory alloys (SMAs) is presented. The strain is separated into elastic, thermal, transformation and plastic strain parts, and two yield functions are adopted to describe respectively the transformation and plastic deformation. An integral algorithm is suggested, including the update of the stress and the tangent stiffness. Numerical examples and the comparison with experimental results show that the proposed approach can well describe the behavior of the SMAs subjected to complicated thermal-mechanical loading, demonstrating the validity of the model in the description of the constitutive behavior of SMAs, including shape memory effect, pseudoelasticity, coupled transformation and plastic deformation, and effect of plastic deformation on the inverse transformation, etc. The corresponding user material subroutine UMAT is developed and embedded into FE code ABAQUS, with which the installation process of SMA pipe joints is simulated and the residual contact pressure between connected pipes and the joint is predicted.


Cite This Article

B. . Chen, X. . Peng, X. . Chen, J. . Wang, H. . Wang et al., "A three-dimensional model of shape memory alloys under coupled transformation and plastic deformation," Computers, Materials & Continua, vol. 30, no.2, pp. 145–176, 2012.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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