Design-oriented modelling of composite actuators with embedded shape memory alloy

Abstract

Shape memory alloy (SMA) actuators have generated a great deal of interest in recent years due to their reusability and ability to exhibit a wide spectrum of actuation properties. In this work we present an analytical approach through which one may predict the actuation stroke as well as recovery potential of a two-component SMA-based composite actuator. The predictions of the analytical model were validated using Finite Element (FE) simulations on a composite SMA actuator designed in the form of an SMA strip embedded within an elastic matrix, where the shape memory effect of the SMA component was modelled using the numerical Souza-Auricchio model. The results obtained from the two approaches show extremely good agreement. The trends found upon altering various geometric and material parameters within the system provide a thorough understanding of how one can vary these parameters in order to obtain a tailored actuation and recovery response from the SMA-based actuator.

Introduction

Shape memory alloys (SMAs) are materials that ‘remember’ their shape after loading and return to their original conformation after heating [1], [2], [3], [4], [5]. This effect comes about due to a phase transition from the cold martensitic phase to the hot austenitic phase and makes these materials ideal for a number of applications [6] such as stents [7], [8], [9], [10], sensors [11], [12] and sports apparel including golf clubs [13], [14]. SMAs have also been implemented in composite structures in order to enhance the functionality of such systems [15], [16], [17]. Another field in which SMAs have generated a great deal of interest is that of actuation. SMA-based actuators have the potential to exhibit a wide range of actuation properties ranging from high force/low stroke ratios for SMA wires to low force/high stroke ratios for SMA spring-based systems [18], [19], [20], [21]. Typical SMA actuators are designed as two component systems incorporating an agonist-antagonistic relationship. The counterbalance effect provided by the additional component to the system besides the SMA part may come about in various forms, including a fixed load, an elastic material or even an opposing SMA system, and its main function is to impart reusability to the SMA actuator [22], [23], [24], [25], [26], [27], [28].

One method to produce such two-component SMA actuators is by embedding SMA wires in a matrix [29], [30], [31], [32]. This technique involves stretching an SMA wire and forming a matrix by pouring the uncured resin around the pinned, stretched wire. Once the resin cures and the matrix is formed, the wire is released and the system equilibrates at a fixed displacement point, provided that there is a good level of adhesion between the matrix and the wire. One may obtain an actuation effect from this composite system by heating the wire. Then, once the system is cooled, the matrix, which acts as a counterbalance to the SMA wire, forces the actuator to return to its original equilibrium point, hence reversing the contraction of the wire and making the actuator reusable.

The efficacy of an SMA composite actuator is dependent primarily on the relative stiffnesses of the counterbalance and the SMA component [26], [28]. If the counterbalance component is too stiff, then the SMA component will not be able to return to its original size when heated. On the other hand, if the counterbalance is too soft, it will not be able to reverse the actuation of the SMA component, rendering the actuator unsuitable for multiple usage. These problems highlight the delicate balance which one must consider when designing a SMA composite actuator.

In view of this, in this work, we present a method through which one may design and optimize the geometry of an SMA composite actuator in order to obtain a tailored stroke based on the individual force-displacement curves of the SMA and counterbalance components of the system. An analytical model which can predict the actuation output and recovery of the actuator was derived and validated using Finite Element (FE) simulations. This model is expected to facilitate the pre-design of SMA composite actuators by quantifying the relationship between the material properties of the individual components of the composite and the geometric parameters of the system. This model also improves on previous models found currently in literature [22], [33] by considering the recovery potential of the actuator and by considering the force-displacement behaviour of the martensitic SMA in terms of three distinct regions rather than as one linear model.