Numerical simulation of shape memory alloys

Abstract
A macroscopic model of the behaviour of polycrystalline SMA is build to be implemented into a finite element code. It is based on a thermodynamical approach of the martensitic phase transformation. To obtain an explicit expression of the Gibbs free energy of a Representative Volume Element of SMA, the stored elastic energy is analysed. Two levels of incompatibility are distinguished: intragranular interaction between austenite and variants of martensite, and intergranular interaction between transformed grains. This micromechanical analysis is simplified to derive an analytical description of the polycrystalline behaviour. The Gibbs energy is then defined as a function of the stress and temperature which are the control variables and of two internal variables: the martensitic volumic fraction and the mean transformation strain over the transformed volume. The behaviour of the SMA is derived from this thermodynamical potential and integrated into the finite element code ABAQUS using subroutine UMAT. Comparisons of the calculation with characterisation tests are concluding, and the example of a structure, a three point bending beam, is shown.