Coupled thermomechanical modelling of shape memory alloy structures undergoing large deformation

Abstract

Shape Memory Alloys (SMAs) exhibit strain recovery capabilities even after undergoing large deformation, out of underlying stress and temperature dependent diffusionless martensitic transformation. Modelling its behaviour accurately requires coupled thermomechanical analysis, considering absorption and emission of latent heat during phase transformation, thermoelastic effects, thermomechanical loading and boundary conditions. Moreover, the variation of material properties, e.g., modulus of elasticity and thermal expansion coefficient, during phase transformation, significantly affects the response of the system. In addition, appropriate stress and strain measures are required to model the large deformation of SMA-based components under practical thermomechanical loads. In this study, a nonlinear finite element formulation based on Total Lagrangian (TL) approach has been developed to address geometric as well as material non-linearity arising out of the SMA behaviour. Furthermore, considering all the above-mentioned effects, both the stress and thermal equilibrium equations are solved simultaneously in an incremental–iterative finite element (FE) framework, simulating the coupled SMA response. The SMA constitutive model, using Green–Lagrange strain and Second Piola–Kirchhoff stress measures, proposed by Qidwai and Lagoudas (2000), has been implemented. Using the developed FE model, the thermomechanical responses of SMA wire actuator, beam and biomedical staple are simulated to demonstrate the need for the coupled analysis while considering large deformation of the SMA structures.