Effective anisotropic elastic constants of bimaterial interphases: comparison between experimental and analytical techniques

Abstract

The effective elastic constants of a bimaterial composite were experimentally measured with the goal of validating the numerical predications of these constants made by homogenization theory. Secondly, solutions predicted by homogenization theory were compared to predictions made with more standard composite theories. Composite specimens consisting of titanium and epoxy were developed to mimic a porous titanium/tissue interphase. Tensile and shear tests (ASTM D3983) measured the stiffness along the porous coating/epoxy interphase ( E L ), across the interphase ( E T ) and in shear ( G LT ). No significant differences in moduli were found between the experimental measurements and predictions made with homogenization theory, nor between the experimental measurements and Hashin-Shtrikman estimates. Homogenization theory predicted results usually within 20% of Hashin-Shtrikman estimates, but typically more than 50% different from what is predicted by the rule of mixtures. However, homogenization theory allows calculation of anisotropic stiffness estimates and local strains, neither of which is possible using Hashin-Shtrikman estimates. With this experimental validation, the accuracy of homogenization theory for use in implant/tissue interface mechanics applications is confirmed. Since the composite interphase is anisotropic and more compliant in the transverse direction, with stiffness an order of magnitude lower across the interphase, local mechanics, tissue ingrowth and remodeling may be strongly directional dependent.