Finite – element model for simulations of fully coupled thermomechanical processes in shape memory alloys

Abstract
The Müller-Achenbach-Seelecke model for shape memory alloys is able to address full thermomechanical coupling of mechanical and thermal fields. The model roots in a stringent interpretation of thermodynamical principles and interprets the behavior as resulting from an interplay of austenite with two generic martensite twin variants. Its constitutive behavior covers both pseudoplasticity, pseudoelasticity and the characteristic shape memory effect upon temperature changes. Thus, the model reflects the complex, nonlinear hysteretic and thermomechanically coupled material behavior of SMAs on a physically sound basis.
In this contribution we investigate the capability of the MAS model in a typical engineering setting, viz. the shrink fitting of a SMA bushing onto a linear-elastic shaft. In this case, the shrink fitting is caused by a martensite-austenite phase transition of the bushing upon temperature change from low to high level (shape memory effect). To address all geometrical implications we employ a finite-element implementation of the MAS model into ABAQUS^TM. The reliability of the FEM model is proven by comparison to the classical solutions for the linear-elastic and the ideally elastic-plastic case. The MAS model is implemented into ABAQUS using the UMAT interface. The results arrived at with this model are validated against the classical solutions and show the significance for the full thermomechanical coupling which becomes particularly evident in this setting.