Finite deformation higher-order plate elements for shape memory alloy constitution

This work focuses on a finite element model for the analysis of plate structures constituted of shape memory alloy material at finite strains. A three dimensional constitutive model [1] for shape memory alloys in the framework of finite strains which is capable of describing the typical macroscopic effects of SMA, as the pseudo-elasticity and the shape memory effect is adopted. The structural model is formulated with a 2D plate theory where the midsurface and the covariant components of kinematic quantities are approximated element-wise with the standard isoparametric approach [2]. The displacement field assumption is based on the classical expansion in thickness direction in terms of increasing powers of the transverse coordinate and leads to an analogous form for the deformation gradient. The equilibrium statement is formulated considering the Virtual Work Principle in the total Lagrangian format. The proposed formulation is suitable for the simple derivation of high-order elements in a fully compatible fashion.