Nonlinear shape optimization of flexible mechanical metamaterials

Abstract

Shape optimization is used to design flexible mechanical metamaterials. We employ the higher-order moving-mesh method to arbitrarily parameterize the geometries and tune their nonlinear mechanical response to our liking under different loading conditions. Rather than considering periodic unit cells, we focus on finite size elastomeric sheets with an embedded array of pores subjected to uniaxial tension, compression, and shear and use the optimization algorithm to tune either their stress–strain response or their effective Poisson’s ratio. We find that for all considered targets the algorithm converges to aperiodic geometries that are non-intuitive and comprise domain-like features. As such, our results indicate that aperiodicity may provide new opportunities for the design of flexible metamaterials.