A morphological elastic model of general hexagonal columnar structures

A general three-dimensional (3D) anisotropic hexagonal model of columnar st ructure with non-uniform strut morphology is developed. This model covers s everal types of cellular structure such as two-dimensional (2D) hexagonal a nd square honeycombs, and 3D hexagonal and rhombic cellular materials of ro d-like columnar structure. The effective elastic constants are determined t aking account of bending, axial, and shear deformations of the struts. Unli ke the theoretical work of other investigators for 2D honeycombs, consideri ng bending, axial and shearing deformations of struts, the present model no t only produces transverse isotropy for regular hexagonal columnar structur e but also provides a consistent Poisson's ratio when applied to a square h oneycomb. The effect of tapered strut morphology on the elastic properties of cellular structures is investigated. For the general hexagonal columnar structures, the bending compliance is the dominant function for the in-plan e elastic constants of 2D and 3D structures (excluding the in-plane shear m odulus of rhombic structures) and the out-of-plane shear moduli of 3D struc tures, but the axial compliance is dominant for the in-plane shear modulus of 2D and 3D rhombic structures and the out-of-plane Young's modulus of 3D structures. For cellular materials with the same relative density, the pres ence of taper increases values of the affective Young's and shear moduli fo r which the bending compliance is dominant, but decreases those for which t he axial compliance is dominant. Tt is found that the effective elastic pro perties of cellular materials are dependent not only on the relative densit y but also on strut morphology both in cross-section geometry and its varia tion along the strut length which the present model takes account of. These results illustrate the importance of the strut morphology in calculating t he effective elastic properties of cellular materials, (C) 2001 Elsevier Sc ience Ltd. All rights reserved.