In this paper, the modeling of the mechanical constitutive relation during stress-induced transitions of shape memory alloys (SMAs) is discussed based on mixture theory. When the initial state of SMA material was a mixture of austenite parents and twinned martensite variants, external stresses for this material would induce both the reorientation from twinned martensite variants to detwinned martensite variants and the transformation from austenite parents to detwinned ones. Corresponding internal variables to describe these transitions are newly defined. This model enables the numerical prediction of the overall mechanical behavior of SMA materials in the temperature range from M_s to M_f. The approach of mixture theory; a series model is applied in the formulation of the constitutive behavior of SMAs with isostress conditions. Tensile tests have been carried out with Ti-Ni specimens in a temperature range including martensite transformation temperatures. Numerical simulation based on the proposed model accurately predicted the mechanical behavior of stress-induced transitions in the concerned temperature range.

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