Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model

Objective. To develop a biomechanical model for cartilage which is capable of capturing experimentally observed nonlinear behaviours of cartilage and to investigate effects of collagen fibril reinforcement in cartilage. Design. A sequence of 10 or 20 steps of ramp compression/relaxation applied to cartilage disks in uniaxial unconfined geometry is simulated for compar ison with experimental data. Background. Mechanical behaviours of cartilage, such as he compression-offs et dependent stiffening of the transient response and the strong relaxation component, have been previously difficult to describe using the biphasic m odel in unconfined compression. Methods. Cartilage is modelled as a fluid-saturated solid reinforced by an elastic fibrillar network. The latter, mainly representing collagen fibrils , is considered as a distinct constituent embedded in a biphasic component made up mainly of proteoglycan macromolecules and a fluid carrying mobile i ons. The Young's modulus of the fibrillar network is taken to vary linearly with its tensile strain but to be zero for compression. Numerical computat ions are carried out using a finite element procedure, for which the fibril lar network is discretized into a system of spring elements. Results. The nonlinear fibril reinforced poroelastic model is capable of de scribing the strong relaxation behaviour and compression-offset dependent s tiffening of cartilage in unconfined compression. Computational results are also presented to demonstrate unique features of the model, e.g. the matri x stress in the radial direction is changed from tensile to compressive due to presence of distinct fibrils in the model.