Programming shape-morphing electroactive polymers through multi-material topology optimisation - Antonio Gil (Applied Mathematical Modelling, 2023)
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 multilayeredDE 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 themultiple layers of the device, is pursued. The resulting layout permits the generation of a heterogenous electricfield within the device due to the spatial variation of the material properties within the layers and across them. Anin-silico or computational approach has been developed in order to facilitate the design of new prototypes capableof displaying predefined electrically induced target configurations. Key features of this framework are: (i) use ofa standard two-field Finite Element implementation of the underlying partial differential equations in reversiblenonlinear electromechanics, where the unknown fields ot the resulting discrete problem are displacements andthe scalar electric potential; (ii) introduction of a novel phase-field driven multi-material topology optimisationframework allowing for the consideration of several DE materials with different material properties, favouring thedevelopment of heterogeneous electric fields within the prototype. This novel multi-material framework permits, forthe first time, the consideration of an arbitrary number of differentNDE materials, by means of the introductionofN−1 phase-field functions, evolving independently over the different layers across the thickness of the devicethroughN−1 Allen-Cahn type evolution equations per layer. A comprehensive series of numerical examplesis analysed, with the aim of exploring the capability of the proposed methodology to propose efficient optimaldesigns. Specifically, the topology optimisation algorithm determines the topology of regions where different DEmaterials must be conveniently placed in order to attain complex electrically induced configurations.