Apparent behaviour of charged and neutral materials with ellipsoidal fibre distributions and cross-validation of finite element implementations

Continuous fibre distribution models can be applied to a variety of biological tissues with both charged and neutral extracellular matrices. In particular, ellipsoidal models have been used to describe the complex material behaviour of tissues such as articular cartilage and their engineered tissue equivalents. The choice of material parameters is more difficult than in classical anisotropic models and the impact that changes to these parameters can have on the predictions of such models are poorly understood. The objective of this study is to demonstrate the apparent behaviour of this class of materials over a range of material parameters. We further introduce a scaling approach to overcome certain counter-intuitive aspects related to the choice of anisotropy parameters and outline the integration method used in our implementations. User material codes for the commercial FE software packages Abaqus and MSC Marc are provided for use by other investigators. Cross-validation of our code against similar implementations in FEBio is also presented.