Multi-resolution methods for the topology optimization of nonlinear electro-active polymers at large strains

This work presents a numerical study on the use of multi-resolution strategies for the computationally challenging problem of optimal design of high-resolution nonlinear electro-active shell-type devices using Topology Optimization methods. This paper puts forward the following novelties. First, it presents a tailor-made in-plane multi-resolution technique where a higher level of resolution for the density field is permitted within the in-plane surface of the electro-active material. Second, a numerical study is carried out to elucidate the lower bound for the critical ratio between the density resolution level (or the number of density voxels within every element of the coarse analysis mesh) and the filtering length that can be used to avoid the presence of QR-patterns in the unexplored scenario of nonlinear electromechanics, without compromising the computational efficiency of the multi-resolution scheme. The numerical experiments illustrate the benefits of the proposed methodology to obtain high-resolution designs with a reasonable computational cost and reveal the possibility for more flexible bounds for the critical ratio as those reported in linear elasticity.