Density-based topology optimisation considering nonlinear electromechanics

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 pm and pe, respectively), featuring in the energy interpolation scheme. Third, it reports that, in contrast to the context of linear piezoelectricity, a choice of pe < pm must be avoided, as this fosters the sudden development of artificial instabilities, compromising the robustness.