A novel computational modelling to describe the anisotropic, remodelling and reorientation behaviour of collagen fibres in articular cartilage - Cortez, Sara (2018)
In articular cartilage the orientation of collagen ﬁbres is not uniform varying mostly with the depth of the tissue. Besides, the biomechanical response of each layer of the articular cartilage diﬀers from the neighbouring ones, evolving through thickness as a function of the distribution, density and orientation of the collagen ﬁbres. Based on a ﬁnite element implementation, a new continuum formulation is proposed to describe the remodelling and reorientation behaviour of the collagen ﬁbres under arbitrary mechanical loads. The cartilaginous tissue is modelled based on a hyperelastic formulation, being the ground isotropic matrix described by a neo-Hookean law and the ﬁbrillar anisotropic part modelled by a new anisotropic formulation introduced for the ﬁrst time in the present work, in which both reorientation and remodelling are taken into account. To characterize the orientation of ﬁbres, a structure tensor is deﬁned to represent the expected distribution and orientation of ﬁbres around a reference direction. The isotropic and anisotropic constitutive parameters were determined by the good validation of the numerical models with the experimental data available from the literature. Considering the eﬀect of realistic collagen ﬁbre reorientation in the cartilage tissue, the remodelling algorithm associated with a distribution of ﬁbres model showed accurate results with few numerical calculations.