Elastic constants and material stability analysis of orthotropic titanium-based metal foams

Abstract

Metallic foams have emerged as promising materials for mitigating the adverse effects of implants on surrounding tissues by replicating the stiffness and structural symmetry of bone. In current fabrication technologies, porosity is widely recognized as the primary topological factor for tuning stiffness and strength. However, as an isotropic parameter, porosity inadequately captures the influence of mesoscale structures on the elastic anisotropy of metallic foams. This study aims to address these limitations by investigating the role of porosity as a topological descriptor in determining elastic constants for anisotropic metallic foams. The research presents a methodology for determining the effective macroscopic elastic constants of orthotropic, titanium-based metal foams across varying porosities, ranging from 5% to 65%, which aligns with the pore size distributions of specimens fabricated via powder metallurgy. Employing genetic algorithm optimization based on Voronoi tessellations, 3D randomized cubic representative volume elements (RVEs) were generated to replicate pore statistics obtained from 2D μCT reconstructions of real foams. Finite element simulations were conducted on these RVEs, including tensile and shear tests, to quantify their mechanical response. Results reveal a general reduction in Young’s modulus, shear modulus, and bulk modulus as porosity increases. Notably, elastic constant dispersion significantly widened at higher porosity levels, with Poisson’s ratio displaying substantial variation in the range of -0.01 < ν < 0.37 at 65% porosity. Zener ratios indicated near-isotropic behavior up to 30% porosity, but microstructural stability sharply declined beyond 65%, as reflected by nearly zero determinants of the stiffness tensors. These findings underscore the critical sensitivity of elastic properties, particularly Poisson’s ratios, to microstructural architecture, providing insights into potential instabilities in highly porous, bone-like cellular structures.