## Abstract

Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen fibril network. The microstructural properties of the collagen network contribute to continuum mechanical tissue properties that are strongly anisotropic with tensile-compressive asymmetry. In this study, a novel approach based on a continuous distribution of collagen fibril volume fractions is developed to model fibril reinforced soft tissues as nonlinearly elastic and anisotropic material. Compared with other approaches that use a normalized number of fibrils for the definition of the distribution function, this representation is based on a distribution parameter (i.e. volume fraction) that is commonly measured experimentally while also incorporating pre-stress of the collagen fibril network in a tissue natural configuration. After motivating the form of the collagen strain energy function, examples are provided for two volume fraction distribution functions. Consequently, collagen second-Piola Kirchhoff stress and elasticity tensors are derived, first in general form and then specifically for a model that may be used for immature bovine articular cartilage. It is shown that the proposed strain energy is a convex function of the deformation gradient tensor and, thus, is suitable for the formation of a polyconvex tissue strain energy function.

Original language | English |
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Pages (from-to) | 706-715 |

Number of pages | 10 |

Journal | Mathematics and Mechanics of Solids |

Volume | 16 |

Issue number | 7 |

DOIs | |

Publication status | Published - Sep 2011 |

## Keywords

- articular cartilage
- collagen fibril network
- distribution function
- polyconvexity
- volume fraction

## ASJC Scopus subject areas

- Materials Science(all)
- Mathematics(all)
- Mechanics of Materials