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 behaviour. The analysis is restricted to small strains, plane problems and monotonic proportional loads. An important feature of this work is the quasi-static frictional contact analysis of the microstructure composed of deformable elastic bodies by means of parametric quadratic programming principle and its corresponding algorithmic implementation. The generality of the homogenisation algorithm, which, in principle, can be applied to a large variety of non-linear behaviour affecting the representative volume element, is clearly described. Numerical examples are given to demonstrate the efficiency and validity of the algorithm presented in the paper.