J. Phys. IV France 11 (2001) Pr5-145-Pr5-152
Gradient-enhanced computational homogenization for the micro-macro scale transitionM.G.D. Geers, V. Kouznetsova and W.A.M. Brekelmans
Faculty of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 Eindhoven, The Netherlands
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.
© EDP Sciences 2001