Nonlinear behaviour and homogenization of metaplates

Large deflections in thin plates introduce a nonlinear membrane-flexural coupling which significantly modifies the plate behaviour under transversal and in-plane loadings. This effect is often important when considering metamaterial plates with periodically distributed heterogeneities or holes. In this work, we employ the asymptotic homogenization technique to study the effective nonlinear behaviour of periodic Föppl-von Kármán plates in the static regime. Then, we validate the method by simulating the nonlinear response of the perforated plate (backplate) which is present in a micro-electro-mechanical microphone to limit the displacements of the vibrating membrane.