Modeling large deformations of thin-walled SMA structures by shell finite elements

Abstract

Abstract Many shape memory alloy (SMA) applications, such as biomedical devices, electromechanical actuators, and elastocaloric cooling devices, are based on thin-walled flat or shell-like structures. An advanced design of such structures requires the development of an efficient and accurate numerical tool for simulations of very thin and curved SMA structures that may experience large deformations and even buckling upon thermo-mechanical loading. So far, finite element models for finite strain deformations of SMA structures have been based on 3D solid formulations, which are relatively inefficient for solving (thin) shell problems. In this paper, we present a finite element model for the analysis of shape memory alloy shells. Our model is based on a 7-parameter, large-rotation, one-director shell formulation, which takes into account a fully three-dimensional form of the constitutive equations for the isothermal transformations of isotropic superelasticity, as well as the shape-memory effect in a simplified way. In fact, we present three 4-node shell finite elements for SMAs. Two of them use the assumed natural strain concepts for the transverse shear strains, through-the-thickness normal strain, and membrane strains. The third element is a combination of the assumed natural strain and the enhanced assumed strain concepts, applied to satisfy the zero through-the-thickness-normal-stress condition for thin geometries to a high degree of accuracy. After a detailed description of the SMA finite element models for shells in the first part of the paper, numerical examples in the second part illustrate the approach. Compared to 3D solid SMA formulations, our results show excellent accuracy, even with a significantly reduced number of degrees of freedom, which consequently translates into a reduction in the computational time.