Variational Reduced-Order Modeling of Thermomechanical Shape Memory Alloy Based Cooperative Bistable Microactuators

Abstract

This article presents the formulation and application of a reduced-order thermomechanical finite strain shape memory alloy (SMA)-based microactuator model for switching devices under thermal loading by Joule heating. The formulation is cast in the generalized standard material framework with an extension for thermomechanics. The proper orthogonal decomposition (POD) is utilized for capturing a reduced basis from a precomputed finite element method (FEM) full-scale model. The modal coefficients are computed by optimization of the underlying incremental thermomechanical potential, and the weak form for the mechanical and thermal problem is formulated in reduced-order format. The reduced-order model (ROM) is compared with the FEM model, and the exemplary mean absolute percentage errors for the displacement and temperature are 0.973% and 0.089%, respectively, with a speedup factor of 9.56 for a single SMA-based actuator. The ROM presented is tested for single and cooperative beam-like actuators. Furthermore, cross-coupling effects and the bistability phenomenon of the microactuators are investigated.

Keywords

• microactuators
• shape memory alloy
• thermomechanics
• reduced-order modeling
• proper orthogonal decomposition