The interplay between martensitic phase transformation, martensite reorientation and dislocation slip in shape memory alloys (SMA) poses a challenge for theoretical description and modeling on all dimensional scales. Interactions of these processes may give rise to complex coupled phenomena such as transformation-induced plasticity or stabilization of martensite through plasticity. Although such effects often degrade the functional behavior of SMA, they can be also exploited in new technology paths leading to smarter product design.

The continuum thermodynamics-based models can help accelerate functional and design development. Formulation of the models within some variational framework can be advantageous especially when multiple deformation processes mutually interact. This approach relies on description of microstructural changes by additional internal variables and formulation of functions related to energy conservation and dissipation in the material in terms of these variables. The time evolution of the material response is then recovered through a combination of minimization problems, which allows to treat both coupled and decoupled processes. The numerical treatment and algorithmic implementation of this type of models into the finite element method is possible through methods borrowed from mathematical optimization.

In this contribution, we will illustrate such an approach on rate-independent constitutive models of the thermomechanical response of polycrystalline Ti-Ni and β-Ti SMA, in which coupled transformation and plasticity processes occur. The models have been validated by comparing the predicted response with experimental data in the stress-strain-temperature space. We have also implemented them in the finite element software and conducted several computational simulations of 3D components to assess their performance.