Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments

Abstract

In 1990, Holmes and Mow [Journal of Biomechanics 23, 1145-1156] developed a hyperelastic biphasic theory to describe finite deformation behaviors of articular cartilage. To date, however, no experimental finite deformation studies have been made to assess the ability of this constitutive model to describe its finite deformation behaviors (e.g. kinetic creep and stress-relaxation, and equilibrium responses). The objectives of this study are: (1) to investigate whether this hyperelastic biphasic theory can be used to curve-fit the finite deformation compressive stress-relaxation behavior of the tissue, and from this procedure, to calculate its material coefficients; and (2) to investigate whether the theory, together with the calculated material coefficients, can accurately predict the outcome of an independent creep experiment followed by cyclical loading of the tissue. To achieve these objectives, circular cylindrical cartilage plugs were tested in confined compression in both stress-relaxation and creep experiments. Results demonstrated that curve-fits of the stress-relaxation experiments produced nonlinear generalized correlation coefficients of r2 = 0.99 +/- 0.02 (mean +/- standard deviation); theoretical predictions of the creep test differed on average by 10.0% +/- 2.0% relative to experimental results. When curve-fitting the creep experiments as well, it was found that the permeability coefficients differed from those obtained from the stress-relaxation experiments (k0,cr = 2.2 +/- 0.8 x 10(-15) m4 N-1 s-1 and Mcr = 0.4 +/- 0.8 vs k0,sr = 2.7 +/- 1.5 x 10(-15) m4 N-1 s-1, and Msr = 2.2 +/- 1.0); these differences may be attributed to imprecisions in the curve-fitting procedure stemming from the low sensitivity of the stress-relaxation and creep behaviors to large variations of M in the permeability function. Advantages and limitations of this theoretical model are presented in the text.