Poroelastic materials reinforced by statistically oriented fibres – numerical implementation and application to articular cartilage.

*(English)*Zbl 1299.74171
IMA J. Appl. Math. 79, No. 5, 1027-1059 (2014); erratum ibid. 80, No. 1, 233-234 (2015).

Summary: This work provides a method for the Finite Element implementation of a previously developed large deformation model for porous fibre-reinforced materials with statistically oriented fibres. The model, which includes a description of the elastic properties and the permeability, was implemented in the open source Finite Element package FEBio, and a number of different simulations were performed to verify the correctness and the robustness of the implementation. In a benchmark test, with statistical, anisotropic but homogenous fibre orientation, the simulations showed that the fluid flow along the dominant fibre direction is significantly larger than across the impermeable, reinforcing fibres, as suggested by previous experimental results and predicted by the theory. Furthermore, as an example of practical application, a realistic articular cartilage model, with statistical and depth-dependent fibre orientation was implemented, and an unconfined compression test was simulated. This could be regarded as the first full, realistic model of articular cartilage in which the effect of the statistically oriented collagen fibres was accounted for not only for the elastic properties, but also for the permeability.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

76S05 | Flows in porous media; filtration; seepage |

76D07 | Stokes and related (Oseen, etc.) flows |

74L15 | Biomechanical solid mechanics |

74B99 | Elastic materials |

76M10 | Finite element methods applied to problems in fluid mechanics |