A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite

The present work addresses a one-dimensional model able to reproduce the shape-memory-alloy superelastic behavior, taking into account the different elastic properties between austenite and martensite. The model is based on a single scalar internal variable, the martensite fraction, for which evolutionary equations in rate form are proposed. The dependency of the elastic modulus in terms of the martensite fraction is computed through different homogenization techniques. Integration in time leads to the time-discrete evolutionary equations, for which a detailed analysis in terms of admissible roots is presented, together with the expression of the consistent tangent modulus. The solution of the time-discrete model is approached through a return map algorithm, properly modified for the case of phase transitions of the type occurring in shape-memory materials. Finally, the ability of the model to simulate one-dimensional experimental data is assessed.