Micromechanical Modeling of Honeycomb Structures Based on a Modified Couple Stress Theory

Abstract

A micromechanics model is developed for hexagonal honeycomb structures by using a modified couple stress theory. The formulation is based on structural analysis of repeating units and a homogenization procedure. Both bending and axial deformations of cell walls are considered here, unlike earlier models. The closed-form expressions for five effective in-plane elastic constants (including two Young's moduli, one shear modulus and two Poisson's ratios) of a honeycomb structure are derived in terms of the Young's modulus of the cell wall material and the slenderness (length-to-thickness) ratio of the cell wall. The formulas for two length scale parameters are obtained in terms of the slenderness ratio and thickness of the cell wall, thereby providing a direct measure of the microstructure of the honeycomb. The constitutive relations for the two-dimensional couple stress continuum equivalently representing the discrete honeycomb structure are provided using the five effective elastic constants and two length scale parameters. The numerical results reveal that for honeycombs with small slenderness ratios the effective Young's moduli and shear modulus are strongly dependent on the slenderness ratio. For low-density honeycombs with large slenderness ratios, the effective elastic constants predicted by the current model agree well with those by an existing model that considers only bending deformations.