Meshfree modelling and simulation of the thermomechanical behaviour of shape memoryalloys

Abstract

This paper presents the numerical modelling and simulation of the nonlinearthermomechanical behaviour of shape memory alloys via a meshfree technique. To describethe martensitic phase transformation and related shape memory effect efficiently,a finite strain constitutive model is formulated similar to that from plasticitytheory. The model takes into account the stress and temperature induced phasetransformation in the alloy. Simplified to be a thermoelastic phase transformationproblem, a constitutive integration algorithm developed in plasticity theory isapplied and numerically implemented in the present model. A nonlinear meshfreeprocedure is developed to numerically simulate the shape memory alloy materialbehaviour. The advantage of the present meshfree procedure lies in its ability forlarge deformation analysis, point-based approximation coinciding with point-wisephase transformation, and continuous stress/strain solution benefitting the phasetransformation determination as well as the convergence of the Newton iterationprocedure. Several numerical tests are presented to illustrate the potential of thepresent shape memory alloy constitutive model, the algorithm and the meshfreeprocedure. The process of stress and thermally induced phase transformationcan be captured. Hysteresis loops in the loading and unloading procedure areproduced.