In-silico design of electrode meso-architecture for shape morphing dielectric elastomers - Antonio Gil (Journal of the Mechanics and Physics of Solids, 2021)
This paper presents a novel in-silico tool for the design of complex multilayer Dielectric Elastomers (DEs) characterised by recently introduced layer-by-layer reconfigurable electrode meso-arquitectures. Inspired by cutting-edge experimental work at Clarke Lab (Harvard) Hajiesmaili and Clarke (2019), this contribution introduces a novel approach underpinned by a diffuse interface treatment of the electrodes, whereby a spatially varying electro-mechanical free energy density is introduced whose active properties are related to the electrode meso-architecture of choice. State-of-the-art phase-field optimisation techniques are used in conjunction with the latest developments in the numerical solution of electrically stimulated DEs undergoing large (potentially extreme) deformations, in order to address the challenging task of finding the most suitable electrode layer-by-layer meso-architecture that results in a specific three-dimensional actuation mode. The paper introduces three key novelties. First, the consideration of the phase-field method for the implicit definition of reconfigurable electrodes placed at user-defined interface regions. Second, the extension of the electrode in-surface phase-field functions to the surrounding dielectric elastomeric volume in order to account for the effect of the presence (or absence) of electrodes within the adjacent elastomeric layers. Moreover, an original energy interpolation scheme of the free energy density is put forward where only the electromechanical contribution is affected by the extended phase-field function, resulting in an equivalent spatially varying active material formulation. Third, consideration of a non-conservative Allen-Cahn type of law for the evolution of the in-surface electrode phase field functions, adapted to the current large strain highly nonlinear electromechanical setting. A series of proof-of-concept examples (in both circular and squared geometries) are presented in order to demonstrate the robustness of the methodology and its potential as a new tool for the design of new DE-inspired soft-robotics components. The ultimate objective is to help thrive the development of this technology through the in-silico production of voltage-tunable (negative and positive Gaussian curvature) DEs shapes beyond those obtained solely via trial-and-error experimental investigation.