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-architectures. 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.

本文提出了一种新的硅工具，用于设计复杂的多层介电弹性体 (DE)，其特征是最近引入的逐层可重构电极细观结构。受克拉克实验室（哈佛）Hajiesmaili 和 Clarke（2019 年）的前沿实验工作的启发，该贡献引入了一种以电极的扩散界面处理为基础的新方法，由此引入了空间变化的机电自由能密度，其活性性能与选择的电极细观结构有关。最先进的相场优化技术与经历大（可能极端）变形的电刺激 DE 数值解的最新发展相结合，为了解决寻找最合适的电极逐层细观结构的挑战性任务，从而产生特定的三维驱动模式。本文介绍了三个关键的创新点。首先，考虑使用相场方法对放置在用户定义界面区域的可重构电极进行隐式定义。其次，电极表面内相场的扩展作用于周围的介电弹性体体积，以解释相邻弹性体层内电极存在（或不存在）的影响。此外，提出了一种原始的自由能密度能量插值方案，其中仅机电贡献受扩展相场函数的影响，导致等效的空间变化活性材料配方。第三，考虑用于表面内电极相场函数演化的非保守 Allen-Cahn 类型的定律，适用于当前的大应变高度非线性机电设置。展示了一系列概念验证示例（圆形和方形几何形状），以证明该方法的稳健性及其作为设计受 DE 启发的新软机器人组件的新工具的潜力。最终目标是通过在硅片上生产电压可调（负高斯曲率和正高斯曲率）DE 形状来帮助推动这项技术的发展，而不仅仅是通过反复试验研究获得的那些形状。考虑用于表面内电极相场函数演化的非保守 Allen-Cahn 类型的定律，适用于当前的大应变高度非线性机电设置。展示了一系列概念验证示例（圆形和方形几何形状），以证明该方法的稳健性及其作为设计受 DE 启发的新软机器人组件的新工具的潜力。最终目标是通过在硅片上生产电压可调（负高斯曲率和正高斯曲率）DE 形状来帮助推动这项技术的发展，而不仅仅是通过反复试验研究获得的那些形状。考虑用于表面内电极相场函数演化的非保守 Allen-Cahn 类型的定律，适用于当前的大应变高度非线性机电设置。展示了一系列概念验证示例（圆形和方形几何形状），以证明该方法的稳健性及其作为设计受 DE 启发的新软机器人组件的新工具的潜力。最终目标是通过在硅片上生产电压可调（负高斯曲率和正高斯曲率）DE 形状来帮助推动这项技术的发展，而不仅仅是通过反复试验研究获得的那些形状。适应当前大应变高度非线性机电设置。展示了一系列概念验证示例（圆形和方形几何形状），以证明该方法的稳健性及其作为设计受 DE 启发的新软机器人组件的新工具的潜力。最终目标是通过在硅片上生产电压可调（负高斯曲率和正高斯曲率）DE 形状来帮助推动这项技术的发展，而不仅仅是通过反复试验研究获得的那些形状。适应当前大应变高度非线性机电设置。展示了一系列概念验证示例（圆形和方形几何形状），以证明该方法的稳健性及其作为设计受 DE 启发的新软机器人组件的新工具的潜力。最终目标是通过在硅片上生产电压可调（负高斯曲率和正高斯曲率）DE 形状来帮助推动这项技术的发展，而不仅仅是通过反复试验研究获得的那些形状。