Programming shape-morphing electroactive polymers through multi-material topology optimisation

Abstract

This paper presents a novel engineering strategy for the design of Dielectric Elastomer (DE) based actuators, capable of attaining complex electrically induced shape morphing configurations. In this approach, a multilayered DE prototype, interleaved with compliant electrodes spreading across the entire faces of the DE, is considered. Careful combination of several DE materials, characterised by different material properties within each of the multiple layers of the device, is pursued. The resulting layout permits the generation of a heterogenous electric field within the device due to the spatial variation of the material properties within the layers and across them. An in-silico or computational approach has been developed in order to facilitate the design of new prototypes capable of displaying predefined electrically induced target configurations. Key features of this framework are: (i) use of a standard two-field Finite Element implementation of the underlying partial differential equations in reversible nonlinear electromechanics, where the unknown fields ot the resulting discrete problem are displacements and the scalar electric potential; (ii) introduction of a novel phase-field driven multi-material topology optimisation framework allowing for the consideration of several DE materials with different material properties, favouring the development of heterogeneous electric fields within the prototype. This novel multi-material framework permits, for the first time, the consideration of an arbitrary number of different N DE materials, by means of the introduction of N−1 phase-field functions, evolving independently over the different layers across the thickness of the device through N−1 Allen-Cahn type evolution equations per layer. A comprehensive series of numerical examples is analysed, with the aim of exploring the capability of the proposed methodology to propose efficient optimal designs. Specifically, the topology optimisation algorithm determines the topology of regions where different DE materials must be conveniently placed in order to attain complex electrically induced configurations.