Porohyperelastic finite element model for the kangaroo humeral head cartilage based on experimental study and the consolidation theory

Solid-extracellular fluid interaction is believed to play an important role in the strain-rate dependent mechanical behaviors of shoulder articular cartilages. It is believed that the kangaroo shoulder joint is anatomically and biomechanically similar to human shoulder joint and it is easy to get in Australia. Therefore, the kangaroo humeral head cartilage was used as the suitable tissue for the study in this paper. Indentation tests from quasi-static (10-4/sec) to moderately high strain-rate (10-2/sec) on kangaroo humeral head cartilage tissues were conduced to investigate the strain-rate dependent behaviors. A finite element (FE) model was then developed, in which cartilage was conceptualized as a porous solid matrix filled with incompressible fluids. In this model, the solid matrix was modeled as an isotropic hyperelastic material and the percolating fluid follows Darcy’s law. Using inverse FE procedure, the constitutive parameters related to stiffness, compressibility of the solid matrix and permeability were obtained from the experimental results. The effect of solid-extracellular fluid interaction and drag force (the resistance to fluid movement) on strain-rate dependent behavior was investigated by comparing the influence of constant, strain dependent and strain-rate dependent permeability on FE model prediction. The newly developed porohyperelastic cartilage model with the inclusion of strain-rate dependent permeability was found to be able to predict the strain-rate dependent behaviors of cartilages.