Gradient-enhanced computational homogenization for the micro-macro scale transition

Predicting the macroscopic behaviour of materials on the basis of the mechanics of their microstructure, has been a subject of intensive research in the past decade. A large class of homogenization techniques has been developed to obtain macroscopic descriptions which represent microstructural features. Among these, closed-form homogenization techniques used to obtain macroscopic constitutive relations with their associated effective parameters, are probably best known. This paper focuses on micro-macro coupled homogenization formulations in which a two-level coupled boundary value problem is set up. Such a formulation is particularly efficient for an evolving highly nonlinear and heterogenous microstructure. A higher-order micro-macro framework is established here, which accounts for size effects and more complex microstructural deformation modes. This enrichment opens up new possibilities for the future use of these two-level computational homogenization methods.