A refined analysis of the effective elasticity tensor for general cellular sandwich cores

Abstract The aim of the present study is the determination of the components of the effective elasticity tensor for two-dimensional cellular sandwich cores in consideration of core face sheet constraints. The microstructure is homogenized by means of a strain-energy based RVE concept assuming that strain states, which are equivalent on the macroscopic level, lead to equal strain energy in a representative volume element whether the real microstructure or the quasi-homogeneous “effective” medium is considered. The strain energy can be evaluated analytically if the cellular structure is decomposed into the individual cell wall elements, and assumptions are made for the displacement field of each cell wall. The displacement field of the core is approximated by a weighted superposition of the displacement field of the unconstrained core and an extension of the displacements of the face sheets into the core region. Since the approach is based on a kinematically admissible strain field in conjunction with the principle of minimum strain energy, the results provide rigorous Voigt type bounds for the effective normal and shear moduli. In general, a good agreement of the analytical results and the results of a finite element analysis is observed.

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