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A one-dimensional coupled thermomechanical model is presented for shape memory alloys (SMAs) under non quasi-static loading by defining a Helmholtz free-energy function consisting of strain energy, thermal energy, and the energy of phase transformation. The first law of thermodynamics is used to address the thermomechanical coupling due to the influence of strain rate on the SMA temperature. The convective heat transfer coefficient of an SMA wire is calculated by using temperature-dependent empirical relations, and it is shown that no single empirical formula for the heat transfer coefficient can be applied to obtain experimentally consistent results under different loading conditions. The martensite fraction is decomposed into stress-induced and temperature-induced fractions so that the model is capable of predicting both the shape memory effect and the pseudoelasticity. Cyclic loading, the effect of wire diameter and the variation of dissipated energy with strain rate are studied, and the general features of the responses are found to be in agreement with the experimental observations.

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A three-dimensional microplane constitutive model utilizing statically constrained formulation with volumetric-deviatoric split is presented for shape memory alloys (SMAs). Shear stress within each microplane is described by resultant shear component on the plane. One-dimensional stress-strain laws are used for normal and shear stresses on microplanes by considering suitable adjustments between the macroscopic and the microscopic quantities. The behavior of SMAs under simple and complicated loadings is studied. The model represents interaction between the stress components and the deviation from normality in the case of nonproportional loadings. The results are in good agreement with the existing theoretical and experimental findings.