"Modeling the collagen fibril network of biological tissues as a nonlin" by Reza Shirazi, Pasquale Vena et al. * Home * Search * Browse Collections * My Account * About * Digital Commons Network™ Skip to main content * Home * FAQ * About * My Account * < Previous * Next > * * Home > * Research > * Faculty Research > * College of Engineering > * Mechanical Engineering > * 88 Mechanical Engineering Modeling the collagen fibril network of biological tissues as a nonlinearly elastic material using a continuous volume fraction distribution function Author Info * Reza Shirazi , University of California - San Diego * Pasquale Vena , Politechno di Milano * Robert L. Sah , University of California - San Diego * Stephen M. Klisch , California Polytechnic State University - San Luis Obispo Follow Recommended Citation Postprint version. Published in Mathematics and Mechanics of Solids , Volume 16, Issue 7, September 1, 2011, pages 706-715. The definitive version is available at https://doi.org/10.1177/1081286510387866 . 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. Disciplines Mechanical Engineering Copyright 2011 Sage Publications . Download DOWNLOADS Since December 21, 2011 Included in Mechanical Engineering Commons Share COinS URL: https://digitalcommons.calpoly.edu/meng_fac/88 Search Enter search terms: Select context to search: in this series in this repository across all repositories Advanced Search * Notify me via email or RSS Browse * Disciplines * Collections * Authors Author Corner * Submit LINKS * Cal Poly, San Luis Obispo * Robert E. Kennedy Library * Mechanical Engineering Department Elsevier - Digital Commons Undergraduate Research Commons | Cal Poly Website Accessibility Statement | bepress Accessibility Statement Privacy Copyright