Homogenised properties of composite materials in large deformations

The analysis of the overall mechanical behaviour of heterogeneous materials subject to large deformations is approached in this paper. First the problem of the homogenisation of composite materials made by regular cell assembly and characterised by a representative volume element (RVE) is stated by assuming non linear elastic constituents. The RVE is subjected to an enforced displacement path on its boundary and incremental homogenised moduli, defined in terms of Biot stress, are deduced. Then, micro- and macro-bifurcation criteria on the incremental solution are used to point out the possible unstable configurations of the RVE. Correspondingly, the micro- and macro-failure surfaces of the material are defined inside to the macroscopic strain space in order to detect the validity range of the overall moduli obtained by solving the homogenisation problem. Finally, two different microstructures are analysed and their incremental homogenised elastic moduli are estimated.