4 - Discrete Homogenization of Network Materials

Abstract

An asymptotic homogenization technique is developed in the framework of geometrical nonlinearities to derive the large strains effective elastic response of network materials viewed as repetitive beam networks. A systematic methodology is established, allowing the prediction of the overall mechanical properties of these structures in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network on the overall response of the equivalent continuum. Internal scale effects of the initially discrete structure are captured by consideration of a micropolar effective continuum model. Applications to the large strain response of 3D microstructure of trabecular bone modeled with a prototype hexagonal network geometry exemplify the powerfulness of the proposed method.