Homogenization of random elastic networks with non-affine kinematics



This contribution concerns the mechanics of materials with random network microstructures. It develops a general homogenization approach that allows to link the microscopic deformation of fibers in the disordered network with the macroscopic response of the continuous solid. This link is established by a novel micro-macro relation based on the kinematics of maximal advance paths that constrains the unknown microscopic stretch of fibers with respect to the macroscopic strain. This relation accounts for the topology of the network, in particular, its connectivity and takes for the tetrafunctional networks a clearly interpretable tensorial form. In line with the principle of the minimum averaged free energy the elastic response of the network is obtained by the relaxation of the variable fiber stretch subjected to the kinematic constraint. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)