Macroscopic finite element analyses of discretematerials based on directly evaluated micro-macro transitions

Abstract

We consider a homogenized macro-continuum with locally attached microstructure of granules and derive specific micromacro transitions by a consistent transfer of discrete micro-variables to field variables on a continuous macrostructure. Displacements and rotational constraints are imposed on the granules on the defined boundary frame of the microstructure. The constraints for linear displacements and uniform tractions on the surface yield upper and lower bound characteristics for periodic boundary conditions with regard to the aggregate stiffness. Secondly, we perform two-scale analyses where we link simulations on the macro- and the microscales. Therein, coupled boundary-value problems are solved on both scales. The macroscopic homogeneous problem is solved by a finite element method where the material model is implemented using the directly evaluated micro-macro transitions on the basis of the discrete microstructures. Finally, a model problem is investigated to clarify the proposed method. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)