Effective compressive elastic behavior of rhombic dodecahedron structure with and without border constraints

Abstract

The effective compressive elastic modulus of the cellular rhombic dodecahedron structure, with m × n cells in the X- and Y- directions in matrix, has been studied. The effective compressive elastic modulus of the structure without border constraint is a function of m and n; while for the structure with border constraints in the X- and Y- directions it is found unique that is independent of m and n, and is a function of the porosity of the structure. In order to study and understand the range of the effective compressive elastic modulus for the structure without border constraint with explicit expression of the structure parameters, an analytical model has been developed to evaluate the lower and upper bounds. The analytical model is also valid for the structure with double border constraints with a unique modulus. In addition, a finite element method based on beam theory in neglecting shearing effect has been developed for both cases, under the specific boundary conditions used in a unit cell, including finite and infinite numbers of cells m or/and n.As such, the analytical method based on beam theory takes into consideration the finite geometry dimensions and the fictive infinite geometry dimensions. The later gives the upper bound of the effective compressive elastic modulus. The modulus of the structure composed of finite numbers of cells m × n without border constraint is not only a function related to the porosity of the structure, but the geometrical parameters d and b. An experimental test has been fulfilled and compared to the theoretical one with reasonable agreement.