Thermomechanics of martensitic phase transitions in shape memory alloys, I: Constitutive theories for small and large deformations

This article deals with the geometrically linear and nonlinear modeling of martensitic phase transitions in shape memory alloys. A geometrically nonlinear theory is required for the thermomechanical simulation of complex structures like endoscopic devices and stents. However, in certain situations like the simulation of pipe couplers, it is sufficient to apply a geometrically linear theory. In both cases, a free energy function is introduced, evolution equations for internal variables are postulated, and the dependence of the fraction of oriented martensite on the transformation strains is represented by a novel constitutive equation. In all, the developed constitutive theories are able to depict the thermomechanically coupled behavior of shape memory alloys. This is demonstrated in Part II of this article (to appear in this journal, in coauthorship with M. Schafers). For this purpose, the theories are numerically treated in the framework of the finite element method in order to solve initial- boundary- value problems. These illustrate the main features of the constitutive theories by means of numerical test calculations. The results are compared with experimental data.