Coupled Finite Element Simulation of Shape Memory Bending Microactuator

Abstract

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 $$\mu \hbox {m}$$ μ m 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.

A Physics-Based Hybrid Dynamical Model of Hysteresis in Polycrystalline Shape Memory Alloy Wire Transducers

“…As pointed out in [32, Assumption 2], if we choose the values of τ x and V L in a physically meaningful way, the transition probabilities p M A and p M A defined in ( 5) behave approximately as high-gain threshold functions. As a result, (4) becomes responsible for the high numerical stiffness of model (17). Following the analysis in [32], it can be shown that during phase transformation (i.e., ẋM ̸ = 0) the following approximation tightly holds for the polycrystalline model ( 17)…”

“…The hybrid reformulation is grounded on the MAS model structural property defined by ( 19)- (20). Indeed, by using ( 19)- (20), we can compute x M without the need to integrate the stiff equation ( 4), therefore improving the numerical properties of model (17), as shown in the sequel. As a first step, a set of operative modes needs to be identified.…”

“…The slack condition is frequently observed when characterizing quasi-plastic SMA wires as well as in agonist-antagonist SMA actuator applications, in which the unactuated wire loses tension during normal operating conditions, only for regaining it after being re-activated [33]. This effect is not covered by model (17), which becomes inaccurate when σ < 0. To model the slack, we include two additional modes by duplicating AM and MA.…”

“…Various modeling approaches have been proposed for SMA in the literature [11], [12]. On the one hand, physics-based models offer a thermodynamically-consistent framework to describe SMA hysteresis and related physical phenomena [13], [14], [15], [16], [17]. These constitutive models can be effectively used to predict the structural response of complex structures coupled with SMA elements.…”