Computational homogenization for non-linear heterogeneous solids

This chapter presents a computational homogenization strategy, whichprovides a rigorous approach to determine the macroscopic responseof heterogeneous materials with accurate account for microstructuralcharacteristics and evolution. When using this micro-macro strategythere is no necessity to define homogenized macroscopic constitutiveequations, which in case of large deformations and complexmicrostructures, would be generally a hardly feasible task. Instead,the constitutive behaviour at macroscopic integration points isdetermined by averaging the response of the deformingmicrostructure. This enables a straightforward application of themethod to geometrically and physically non-linear problems, makingit a particularly valuable tool for the modelling of evolvingnon-linear heterogeneous microstructures under complex macroscopicloading paths. In this chapter, the underlying concepts and thedetails of the computational homogenization technique are given.Formulation of the microscopic boundary value problem and theconsistent micro-macro coupling in a geometrically and physicallynon-linear framework are elaborated. The implementation of thecomputational homogenization scheme in a finite element framework isdiscussed. Some recent extensions of the computationalhomogenization schemes are summarized.