This work presents a first numerical study for the density-based topology optimisation in the challenging and scarcely explored context of nonlinear electromechanics, focusing on electro-active polymers, capable of undergoing large electrically induced deformations. This paper puts forward the following novelties. First, it presents an energy interpolation scheme for the electromechanical energy functional of solid and void regions. Regarding the latter, it recommends the use of an unconditionally stable definition deferring the development of artificial instabilities. Second, it carries out a numerical study assessing the convenience of different mechanical and electromechanical penalising exponents (denoted as p_m and p_e, respectively), featuring in the energy interpolation scheme. Third, it reports that, in contrast to the context of linear piezoelectricity, a choice of p_e < p_m must be avoided, as this fosters the sudden development of artificial instabilities, compromising the robustness.

这项工作提出了在非线性机电学中极富挑战性和鲜为人知的背景下，基于密度的拓扑优化的首次数值研究，重点是能够经历大的电感应变形的电活性聚合物。本文提出以下新颖性。首先，它提出了一种用于固体和空隙区域的机电能量函数的能量插值方案。关于后者，建议使用无条件稳定的定义，以延缓人为不稳定的发展。其次，它进行了数值研究，评估了不同的机械和机电惩罚指数（分别表示为p _m和p _e）的便利性。，分别以能量插值方案为特色。第三，它报告说，与线性压电的情况相反，必须避免选择p _e < p _m，因为这会促进人为不稳定性的突然发展，从而损害了鲁棒性。