Tuning the elastic nonlinearities in composite nanomaterials

Abstract

The possibility of tuning the nonlinear effective response of composite materials and structures is of great importance for developing new concepts such as soft metamaterials, acoustic diodes, nonlinear waveguides and phononic crystals. In this paper we develop a homogenization technique for dispersions of nonlinear particles in a soft matrix able to take account of second and third order elastic nonlinearities. Based on this method, we prove the possibility to strongly amplify a given particles nonlinearity (either the second or the third one) under specific conditions concerning the linear response of the two constituents (particles and matrix). We finally give a realistic example based on a population of porous polymer particles embedded in a PDMS matrix.