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On Fiber Dispersion Models: Exclusion of Compressed Fibers and Spurious Model Comparisons

Journal of Elasticity volume 129, pages 49–68 (2017)Cite this article

Abstract

Fiber dispersion in collagenous soft tissues has an important influence on the mechanical response, and the modeling of the collagen fiber architecture and its mechanics has developed significantly over the last few years. The purpose of this paper is twofold, first to develop a method for excluding compressed fibers within a dispersion for the generalized structure tensor (GST) model, which several times in the literature has been claimed not to be possible, and second to draw attention to several erroneous and misleading statements in the literature concerning the relative values of the GST and the angular integration (AI) models. For the GST model we develop a rather simple method involving a deformation dependent dispersion parameter that allows the mechanical influence of compressed fibers within a dispersion to be excluded. The theory is illustrated by application to simple extension and simple shear in order to highlight the effect of exclusion. By means of two examples we also show that the GST and the AI models have equivalent predictive power, contrary to some claims in the literature. We conclude that from the theoretical point of view neither of these two models is superior to the other. However, as is well known and as we now emphasize, the GST model has proved to be very successful in modeling the data from experiments on a wide range of tissues, and it is easier to analyze and simpler to implement than the AI approach, and the related computational effort is much lower.

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Authors and Affiliations

  1. Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16-II, 8010, Graz, Austria

    Gerhard A. Holzapfel

  2. Faculty of Engineering Science and Technology, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway

    Gerhard A. Holzapfel

  3. School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland, UK

    Ray W. Ogden

Authors
  1. Gerhard A. Holzapfel
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  2. Ray W. Ogden
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Correspondence to Gerhard A. Holzapfel.

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Holzapfel, G.A., Ogden, R.W. On Fiber Dispersion Models: Exclusion of Compressed Fibers and Spurious Model Comparisons. J Elast 129, 49–68 (2017). https://doi.org/10.1007/s10659-016-9605-2

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  • DOI: https://doi.org/10.1007/s10659-016-9605-2

Keywords

  • Fiber dispersion model
  • Generalized structure tensor
  • Angular integration model
  • Fibrous tissue
  • Exclusion of compressed fibers

Mathematics Subject Classification

  • 74B20
  • 74E10
  • 74L15