A finite-strain constitutive model for anisotropic shape memory alloys

This paper presents a three-dimensional (3D) model to simulate self-accommodation, anisotropic martensitic transformation/orientation, reorientation of martensite variants, asymmetry in tension-compression and phase-change-dependent elastic properties in shape memory alloys (SMAs) within a finite-stain regime. The model is developed based on a multiplicative decomposition of the deformation gradient into elastic and inelastic parts by satisfying the second law of thermodynamics in sense of Clausius-Duhem inequality. The mathematical equations are derived in terms of symmetric tensors simplifying the constitutive relations. The finite-strain model is linearized into the small-strain regime preserving the materially non-linear feature. A description of the time-discrete form of the proposed model and its associated solution algorithm is presented. Numerical simulations of the mechanical behaviors of highly-textured NiTi 3D printed parts, wires and helical springs subjected to simple and complex loadings are performed and compared with experiments. Qualitative and quantitative correlation is observed between simulations and experiments to verify the predictive capabilities of the model and the solution procedure. It is also shown that the finite-strain modeling is essential for accurate prediction of SMA behaviors when deformations are prominent. Due to the absence of similar models in the specialized literature, this paper will fill a gap in the state of the art of this problem, and provide a computationally efficient tool for design and analysis of highly-textured SMA devices under complex loadings.