Non-linear homogenization of polymer composites with porous inclusions

We homogenize the mechanical properties of a two-phase polymer composite, made of a polyurethane matrix containing porous spherical silicone-based inclusions, and designed to be used for wave control as a local resonant insulator. First we consider a homogenized energy for the spherical inclusions, an expression obtained by an explicit method. Then, we couple inclusions and matrix by means of the second-order tangent method. Direct finite element simulations allow some comparisons with available experiments. •Non-linear homogenisation of two-phase composite made of porous spherical inclusions•Explicit energy-based approach for homogenization of spherical inclusions•Second-order tangent method•Validation through comparison with experimental and numerical results