Chapter 9 - SMA constitutive modeling and analysis of plates and composite laminates

Abstract

This chapter focuses on three-dimensional (3D) constitutive modeling for shape memory alloys (SMA) and on finite element analysis of SMA plate and composite laminate devices. The discussion starts with a review of SMA macroscopic constitutive models with internal variables, based on the thermodynamics of irreversible processes. Subsequently, a finite strain 3D constitutive model is presented, together with a small strain constitutive model for composite SMA materials. The homogenization method for the nonlinear composite, the numerical integration procedure of the evolutive equations, and their algorithmic pseudocodification are discussed. A finite strain higher-order plate finite element model based on 3D continuum mechanics is introduced and linked to the corresponding constitutive model; in this regard, a set of exemplary benchmark problems is reported to show the robustness and reliability of the SMA finite element model for the analysis of thermomechanical actuators. Finally, a laminate plate model based on the von Kármán theory is considered and a series of engineering problems is addressed: namely, an analysis of plate-like structural elements with embedded SMA laminae, under various loading conditions, is carried out with the aim of optimizing structural control with respect to buckling phenomena.