An Exact Theoretical Solution for Predicting the Apparent Poisson’s Ratio of Articular Cartilage: A Charged-Hydrated Biological Tissue — The Triphasic Paradigm

The triphasic theory has been successfully used to model the mechano-electrochemical behaviors of soft charged hydrated tissue such as articular cartilage. However, the general equations describing such materials are highly complex and nonlinear. In this study, we have linearized these equations with respect to small strains, and using regular perturbation and similarity methods, analytic solutions have been obtained for the lateral expansion of a cylindrical specimen during the unconfined at both steady state, and at short times. Our results showed that the variation of apparent Poisson’s ratio is only dependent on an important governing parameter ζ, defined by the ratio of osmotic pressure change due to compression to the elastic stress change. From the short-time solution, the lateral expansion decreased with the square root of time.