A Microstructural Model for the Anisotropic Drained Stiffness of Articular Cartilage

Abstract

A constitutive model for articular cartilage is developed to study directional load sharing within the soft biological tissue. Cartilage is idealized as a composite structure whose static mechanical response is dominated by distortion of a sparse fibrous network and by changes in fixed charge density. These histological features of living cartilage are represented in a microstructural analog of the tissue, linking the directionality of mechanical stiffness to the orientation of microstructure. The discretized ‘model tissue’ is used to define a stiffness tensor relating drained stress and strain over a regime of large deformation. The primary goal of this work was to develop a methodology permitting more complete treatment of anisotropy in the stiffness of cartilage. The results demonstrate that simple oriented microscopic behaviors can combine to produce complicated larger scale response. For the illustrative example of a homogeneous specimen subjected to confined compression, the model predicts a nonlinear anisotropic drained response, with inherent uncertainty at cellular size scales.