Implementation of the Mueller – Achenbach – Seelecke model for shape memory alloys in ABAQUS

The temperature rise caused by phase transformations is an integral part of the behavior of shape memory alloys. Among the models capable of incorporating this thermomechanical coupling between the mechanical and thermal constitutive equations is the one by Mueller, Achenbach and Seelecke. Its versatility when implemented as a standalone FORTRAN program has already been documented for single crystals under uniaxial loading.
This code was ported into the 'user material' interface in the commercial finite element package ABAQUS and results validated by comparison with a reference solution for a horizontal cantilever fully restrained at one end and loaded by a vertical point force at its free end.
Further, a more recent extension of the model to uniaxially stretched polycrystalline materials was tackled as these are of greater relevance. The approach roots in the method of 'parameterization' which interprets a polycrystal deformation as being equivalent to the one of a single crystal exposed to varying energy barriers. The computational effort of the single crystal version therefore prevails. Thermal gradients can be resolved even in a small volume.
In the sequel, an outlook is provided on the general case of multiaxial loading.