Topology optimisation of stiffeners layout for shape-morphing of dielectric elastomers

This paper presents an in-silico framework, where for the first time, the design of stiffeners layout for shape-morphing of dielectric elastomers, is carried out by means of topology optimisation (TO). Inspired by the experimental work at Clarke Lab (Harvard) (Hajiesmaili and Clarke in Nat Commun 10(183):1-7, 2019), this paper explores the use of TO techniques with the aim of designing the layers of passive or purely mechanical material that need to be attached to a fixed layer of active dielectric elastomer (DE). The aim is to induce an anisotropic response of the overall device when the active region is subjected to a voltage gradient across its thickness, hence, obtaining complex electrically induced deformations yielding Gaussian curvature changes. The latter can be alternatively achieved by means of the optimisation of spatially varying electrodes (Martinez-Frutos et al 2021) but not through the optimisation of the electro-active material itself (Ortigosa et al in Struct Multidisc Optim 64:257-280, 2019). A series of numerical examples are included in this paper where the objective of the topology optimisation of passive materials over active layers of DEs is demonstrated by inducing desired anisotropy in their response, yielding complex electrically induced deformations. Furthermore, a study of the influence upon the optimised design of the relative mechanical stiffness of the passive material or stiffener with respect to that the non-optimisable electro-active material has been presented in the numerical examples section.