Relaxed loading conditions for higher order homogenisation approaches

Abstract

The present paper deals with the formulation of minimal loading conditions for the application of numerical homogenisation techniques, namely the FE 2 methodology. Based on the set of volume averaging rules connecting the heterogeneous micro and the homogeneous macro scale, the minimal constraints on the deformation of a micro volume are derived for a classical Cauchy continuum as well as for a micromorphic continuum theory. For both cases, numerical studies are included highlighting the main aspects of the proposed procedure within the context of small deformations.