Local analysis and global nonlinear behaviour of periodic assemblies of bodies in elastic contact

This work attempts to capture the effects of microstructural changes on the overall response of a composite made of bodies in elastic contact, and to define numerically a homogenised constitutive relationship for the global b ehaviour. The analysis is restricted to small strains, plane problems and m onotonic proportional loads. An important feature of this work is the quasi -static frictional contact analysis of the microstructure composed of defor mable elastic bodies by means of parametric quadratic programming principle and its corresponding algorithmic implementation. The generality of the ho mogenisation algorithm, which, in principle, can be applied to a large vari ety of non-linear behaviour affecting the representative volume element, is clearly described. Numerical examples are given to demonstrate the efficie ncy and validity of the algorithm presented in the paper.