A conewise linear elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage

A biphasic mixture model is developed that can account for the observed ten sion: compression nonlinearity of cartilage by employing the continuum-base d Conewise Linear Elasticity (CLE) model of Curnier et al. (J. Elasticity, 37, 1-38, 1995) to describe the solid phase of the mixture. In this first i nvestigation, the orthotropic octantwise linear elasticity model was reduce d to the more specialized case of cubic symmetry, to reduce the number of e lastic constants from twelve to four. Confined and unconfined compression s tress-relaxation, and torsional shear testing were performed oa each of nin e bovine humeral head articular cartilage cylindrical plugs from 6 month ol d calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H-(A) =0.64+/-0.22 MPa, k(z)=3.62 +/-0.97X10(-16) m(4)/N .s, r(2) =0.95+/ -0.03), the tensile modulus, compressive Poisson ratio, and radial permeabi lity were obtained from unconfined compression (E(+=)Y12.75 +/-1.56 MPa, up silon - =0.03 +/-0.01, k(r)=6.06+/-2.10X10(-16) m(4)/N .s, r(2) =0.99+/-0.0 0), and the shear modulus was obtained from torsional shear (mu =0.17+/-0.0 6 MPa). The model tvas also employed to pr-edict the interstitial fluid pre ssure successfully at the center of the cartilage plug in unconfined compre ssion (r(2)=0.98+/-0.01). The results of this study demonstrate that the in tegration of the CLE model with the biphasic mixture theory can provide a m odel of cartilage that can successfully curve-fit three distinct testing co nfigurations while producing material parameters consistent with previous r eports in the literature. [S0148-0731 (00)00306-X].