Modeling the collagen fibril network of biological tissues as a nonlinearly elastic material using a continuous volume fraction distribution function

Reza Shirazi, Pasquale Vena, Robert L. Sah, Stephen M. Klisch

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)706-715
Number of pages10
JournalMathematics and Mechanics of Solids
Volume16
Issue number7
DOIs
Publication statusPublished - Sep 2011

Fingerprint

Biological Tissue
Collagen
Elastic Material
Volume Fraction
Distribution functions
Volume fraction
Distribution Function
Tissue
Strain Energy
Strain energy
Modeling
Soft Tissue
Energy Function
Tensors
Tensor
Prestress
Cartilage
Anisotropic Material
Continuous Distributions
Convex function

Keywords

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

ASJC Scopus subject areas

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

Cite this

Modeling the collagen fibril network of biological tissues as a nonlinearly elastic material using a continuous volume fraction distribution function. / Shirazi, Reza; Vena, Pasquale; Sah, Robert L.; Klisch, Stephen M.

In: Mathematics and Mechanics of Solids, Vol. 16, No. 7, 09.2011, p. 706-715.

Research output: Contribution to journalArticle

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