Coupled Finite Element Simulation of Shape Memory Bending Microactuator

Due to their high-energy density, shape memory alloys (SMAs) are investigated as material for bending microactuators in applications of self-folding structures, realizing the concept of programmable matter. Here, for the numerical prediction of the electro-thermo-mechanical performance, the quantification of the time-dependent coupling effects in SMA materials during phase transformation is of crucial interest. Isothermal SMA material models cannot treat the time-dependent interaction between deformation, temperature and electric potential in thermally controlled actuation. In this paper, we extend an isothermal SMA model using standard thermodynamics (Coleman–Noll procedure) to treat the time-dependent behavior of polycrystalline SMAs. The model is implemented as a user material subroutine (UMAT) in a standard finite element (FE) code (Abaqus standard). The time-dependent loading of a tensile sample and a bending microactuator made from 20 μm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \hbox {m}$$\end{document} thick SMA foil are simulated. A comparative study between experimental and simulation results on the thermoelastic and caloric effects during stress-induced phase transformation is presented. Joule heating simulations for shape recovery during both tensile and bending loading are conducted. Time-resolved temperature variations accompanying the loading and Joule heating processes are reported. The coupled SMA material model is found to be capable of approximating the time-dependent field quantities of a polycrystalline SMA microactuator subjected to electro-thermo-mechanical loading.