Phenomenological Constitutive Equations for Numerical Simulations of SMA's Structures. Effects of Thermomechanical Couplings

Abstract
Tension-compression tests at different room temperatures and at different strain rates have been performed on Shape Memory Alloys (CuZnAl, NiTi) using a thermomechanical device. The experiments underline the main role of the temperature variations induced by the deformation process on the stress-strain curves. These variations are essentially due to the latent heat of phase change and the analysis of the associated energy balances shows that the intrinsic dissipated energy remains very small compared to deformation work or latent heat of phase change. On the basis of these results, a behavioral model is proposed that assumes an intrinsic dissipation identically equal to zero and that considere anisothermal deformation processes. This model, written under the formalism of Generalized Standard Materials takes into account the thermoelastic couplings and considers two self-accommodating martensite variants. It is implemented in a finite element code realized to predict the effects of thermomechanical couplings. An implicit integration scheme is used to derive at each step in time the fields stress, strain, temperature, and volume proportions of phases. At each step and due to the thermomechanical coupling, we have to solve non-symmetric linear systems. Numerical simulations are shown first to verify the coherence with the experimental results obtained under uniaxial loading, and secondly to underline the practical interest of such an approach to design SMA's structures.