A nonlinear plate finite element formulation for shape memory alloy applications

The aim of the present work is to develop a new finite element model for the finite strain analysis of plate structures constituted of shape memory alloy (SMA) material. A three-dimensional constitutive model for shape memory alloys able to reproduce the special thermomechanical behavior of SMA characterized by pseudoelasticity and shape memory effects is adopted. The finite strain constitutive model is thermodynamically consistent and is completely formulated in the reference configuration. A two-dimensional plate theory is proposed based on a tensor element shape function formulation. The displacement field is expressed in terms of increasing powers of the transverse coordinate. The equilibrium statement is formulated on the basis of the virtual displacement principle in a total Lagrangian format. The proposed displacement formulation is particularly suitable for the simple derivation of high-order finite elements. Numerical applications are performed to assess the efficiency and locking performance of the proposed plate finite element. Some additional numerical examples are carried out to study the accuracy and robustness of the proposed computational technique and its capability of describing the structural response of SMA devices.