A finite deformation theory for cartilage and other soft hydrated connective tissues--I. Equilibrium results

The determination of valid stress-strain relations for articular cartilage under finite deformation conditions is a prerequisite for constructing models for synovial joint lubrication. Under physiological conditions of high strain rates and/or high stresses in the joint, large strains occur in cartilage. A finite deformation theory valid for describing cartilage, as well as other soft hydrated connective tissues under large loads, has been developed. This theory is based on the choice of a specific Helmholtz energy function which satisfies the generalized Coleman-Noll (GCN0) condition and the Baker-Ericksen (B-E) inequalities established in finite elasticity theory. In addition, the finite deformation biphasic theory includes the effects of strain-dependent porosity and permeability. These nonlinear effects are essential for properly describing the biomechanical behavior of articular cartilage, even when strain rates are low and strains are infinitesimal. The finite deformation theory describes the large strain behavior of cartilage observed in one-dimensional confined compression experiments at equilibrium, and it reduces to the linear biphasic theory under infinitesimal strain and slow strain rate conditions. Using this theory, we have determined the material coefficients of both human and bovine articular cartilages under large strain conditions at equilibrium. The theory compares very well with experimental results.