Numerical implementation of the microplane constitutive model for shape memory alloys

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With the advent of shape memory alloys, several industrial applications were proposed due to their superior mechanical and biological properties. Since the fabrication and characterization of shape memory alloy devices is challenging and expensive, it is necessary to simulate their thermomechanical responses before fabrication. To do so, a powerful constitutive model capable of simulation of the important features of these materials is necessary. To be able to simulate a shape memory alloy device, it is vital to implement a suitable constitutive model in such a way to be used in finite element models. In this paper, an existing constitutive model based on microplane theory is numerically implemented and the effects of stress increment, different numerical integration formulas, and loading direction on the thermomechanical response of shape memory alloy is investigated through superelastic and shape memory proportional and nonproportional loadings. The obtained results show that the stress increment may have significant effect on the results if the forward Euler scheme is utilized. In addition, for the case of numerical integration over the surface of a unit hemisphere, 61 points integration formula without orthogonal symmetry provides the best results while 21 orthogonally symmetric one is the most inaccurate one. Also, the orthogonally symmetric numerical integration formulas predict the isotropic material response while those without orthogonal symmetry predict a little anisotropy.