A two species thermodynamic Preisach approach for simulating superelastic responses of shape memory alloys under tension and bending loading conditions

Modeling superelastic behavior of shape memory alloys (SMA) has received considerable attention due to SMAs ability to recover large strains with associated loading unloading hysteresis enabling them to find many applications. In this work,a simple mechanics of materials modeling approach for simulating superelastic responses of SMA components under tension and bending loading conditions is developed. Following Doraiswamy, Rao and Srinivasa's(1) approach, the key idea here would be in separating the thermoelastic and the dissipative part of the hysteretic response with a Gibbs potential based formulation which includes both thermal and mechanical loading in the same framework. The dissipative part is then handled by a discrete Preisach model. The model is formulated directly using tensile stress-strain or bending moment-curvature rather than solving for non-homogeneous stress and strains across the specimen cross-sections and then integrating the same especially for bending loading conditions. The model is capable of simulating complex superelastic responses with multiple internal loops and provides an improved treatment for temperature dependence associated with superelastic responses. The model results are verified with experimental results on SMA components like wires and beams at different temperatures.