An analytical method to calculate effective elastic properties of mapped rhombic dodecahedron structures fabricated with electron beam melting - Yu, Boning; Li, Yuming; Abbes, Boussad; Li, Shujun; Yu, Baoyi (Materials Today Communications, 2022)
Cellular rhombic dodecahedron (RD) structures fabricated in Ti6Al4V using the electron beam melting (EBM) process have been proposed for tissue scaffolds and medical implants that approximate the properties of bone. The mechanical properties of these structures have often been determined through compressive tests. The introduction of a uniaxial mapping ratio allows structures with personalized parameters and desired mechanical properties to be manufactured with respect to different border constraints without changing the porosity of the structure. In this study, a non-linear relationship between the effective modulus of elasticity and the number of cells was found for periodically arranged RD porous structures, and there were discrepancies in the modulus for different mapping ratios of specimens having the same size. An analytical model based on beam theory is therefore proposed to estimate the effective compressive elastic modulus and Poisson's ratio for such phenomenon. The analytical model predicts cases including 1 × 1 to ∞ ×∞ cells without boundary constraints and arbitrary m× n with boundary constraints, among which the 1 × 1 and ∞ ×∞ cases without boundary constraints give the lower and upper limits of the effective compressive modulus, respectively. The prediction accuracy of m× n cells with analytical solutions was verified by beam elements neglecting shearing effects in the FE method, and both gave identical results under the same constraints. However, the analytical method has advantages that are difficult to replace when dealing with models where the number and dimension of cells far exceed the computational capacity of numerical simulations. Influenced by surface quality, the effective modulus of the actual test is generally between the values predicted by the input-defined inner and outer diameters of the strut as an input.
Keywords: Additive manufacturing; Analytical model; Effective elastic modulus; Mapped rhombic dodecahedron