Effective elastic properties of hexagonal and quadrilateral grid structures

Abstract

The energetic homogenization procedure for the determination of the effective elasticity tensor of grid structures as proposed in an earlier paper is extended to the analysis of general hexagonal and quadrilateral grid structures. The method is based on the assumption that for macroscopically equal deformation the same strain energy has to be stored in a representative volume element whether the given microstructure or the effective homogenized medium is considered. The components of the effective elasticity tensor are determined by partial derivation of the strain energy density with respect to the macroscopic strain components. The analysis is performed comparatively by an analytical approach and by means of the finite element method. Standard commercial sandwich core geometries are considered as well as highly non-orthotropic grid structures. The influence of the cell geometry on the effective properties is discussed in detail. Special interest is directed to negative Poisson's ratios as well as to effectively non-orthotropic elastic behaviour.