Numerical modeling of stress induced martensitic phase transformations in shape memory alloys

Phenomenological models of shape memory behavior are based on either continuum hypothesis (macroscopic) or on volume averages over a representative volume element consisting of several grains. These constitutive models attempt to model the shape memory behavior using maoro/micromechanics and thermodynamics. In general, these models share a common feature. They describe the martensitic phase transformation by a parameter representing the martensite volume fraction, and formulate an evolution law for the martensite volume fraction. Exploiting the similarity of these models to elastoplasticity, we describe a finite element formulation of a micromechanics based constitutive model. Several other models can be formulated in a similar way, and the present work can be seen as a testbed approach to study and evaluate the constitutive models on a common platform. We present numerical results for Au-47.5at%Cd and Ti-50.6at%Ni to validate the finite element formulation. © 1998 Elsevier Science Ltd