Meshfree modelling and simulation of the thermomechanical behaviour of shape memory alloys

This paper presents the numerical modelling and simulation of the nonlinear thermomechanical behaviour of shape memory alloys via a meshfree technique. To describe the martensitic phase transformation and related shape memory effect efficiently, a finite strain constitutive model is formulated similar to that from plasticity theory. The model takes into account the stress and temperature induced phase transformation in the alloy. Simplified to be a thermoelastic phase transformation problem, a constitutive integration algorithm developed in plasticity theory is applied and numerically implemented in the present model. A nonlinear meshfree procedure is developed to numerically simulate the shape memory alloy material behaviour. The advantage of the present meshfree procedure lies in its ability for large deformation analysis, point-based approximation coinciding with point-wise phase transformation, and continuous stress/strain solution benefitting the phase transformation determination as well as the convergence of the Newton iteration procedure. Several numerical tests are presented to illustrate the potential of the present shape memory alloy constitutive model, the algorithm and the meshfree procedure. The process of stress and thermally induced phase transformation can be captured. Hysteresis loops in the loading and unloading procedure are produced.