A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression

The depth dependence of material properties of articular cartilage, known a s the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significanc e of material heterogeneity in the mechanical behavior of cartilage. The ma terial variations proposed are based on extensive observations. The collage n fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Young's modulus and Poisson's ratio of the drained nonfibrillar matrix are so determined th at the aggregate compressive modulus for confined geometry fits the experim ental data. Three nonlinear factors are considered, i.e. the effect of fini te deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features o f the model are then demonstrated with an emphasis on the results obtainabl e only with a nonhomogeneous model, showing reasonable agreement with exper iments. The model suggests mechanical behaviors significantly different fro m those revealed by homogeneous models: not only the depth variations of th e strains which are expected by qualitative analyses, but also, for instanc e, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is n ecessary for better understanding of the mechanical behavior of cartilage. (C) 2000 Elsevier Science Ltd. All rights reserved.