Open Access

ARTICLE

A Constitutive Model for Porous Shape Memory Alloys Considering the Effect of Hydrostatic Stress

Bingfei Liu¹, Guansuo Dui^1,2, Yuping Zhu³

1 Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China
2 Corresponding author. Tel.: +1-86-1051688437; fax: +1-86-1051682094. E-mail addresses: Gsdui@center.njtu.edu.cn
3 Institute of Mechanics and Engineering, Jiangsu University, Zhenjiang 100044, China

Computer Modeling in Engineering & Sciences 2011, 78(3&4), 247-276. https://doi.org/10.3970/cmes.2011.078.247

Abstract

A constitutive model considering the effect hydrostatic stresses induced by porosity on the macroscopic behavior of porous Shape Memory Alloys (SMAs) is developed in this paper. First, a unit-cell model is adopted to establish the constitutive relations for the porous SMAs with SMA matrix and the porosity taken to be voids. Dilatational plasticity theory is then generalized for the SMA matrix. Based on an approximation of the velocity field and the upper bound theory, an explicit yield function for the porous SMA is derived from micromechanical considerations. Finally, an example for the uniaxial response under compression of a porous Ni-Ti SMA material under isothermal condition is supplied by using the dense Ni-Ti SMA parameters. Good agreement between the theoretical predictions of the proposed model and published experimental data is observed, and the model can be available to different porosities.

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