In this work we suggest a new thermomechanically coupled material model for shape memory alloys. In contrast to many earlier concepts of this kind the present approach includes arbitrarily large deformations. The work is motivated by the requirement to carry out finite element simulations of NiTi stents. Depending on the quality of the numerical results it is possible to circumvent, at least partially, expensive experimental investigations. Stent structures are usually designed to significantly reduce their diameter during the insertion into a catheter. Thereby large rotations combined with moderate and large strains occur. In this process an agreement of numerical and experimental results is often hard to achieve. One of the reasons for this discrepancy is the use of unrealistic material models which mostly rely on the assumption of small strains. In the present contribution we derive a new constitutive model which is no longer limited in this way. In the framework of large deformations this model is able to describe pseudoelasticity as well as the shape memory effect. Additionally a phase transformation criterion is introduced which includes the tension-compression asymmetry, typical for shape memory alloys. This transformation criterion depends on the second and third invariant of the deviatoric stress tensor. A further topic of this work is the efficient implementation of the model into a finite element formulation. One of the key issues in this regard is to fulfil ``inelastic'' incompressibility in each time increment. Here we suggest a kind of exponential map where the exponential function is suitably computed by means of the spectral decomposition. A series expansion is completely avoided. Finite element simulations of stent structures show that the new concept is well appropriate to demanding finite element analyses as they occur in practically relevant problems.

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