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Biomechanics: Trends in Modeling and Simulation pp 83–156Cite as

Nonlinear Continuum Mechanics and Modeling the Elasticity of Soft Biological Tissues with a Focus on Artery Walls

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Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 20))

Abstract

This chapter provides a detailed summary of the background from the nonlinear theory of continuum mechanics that is required in the modeling of the elastic properties of soft biological tissues. In particular, it highlights methods for including the fibrous structure of such tissues within the constitutive description of the material properties at the macroscopic level. Of particular relevance in this connection are the so-called preferred directions associated with fibers and the structure tensors and associated deformation invariants that are needed for taking these fibers and their dispersed directions into consideration. These are incorporated into the material models and the effect of fiber structure on the material response is then illustrated with several basic examples. Generalizations of structure tensors are also used for including within the theory the important residual stresses that are evident in unloaded tissues such as arteries and the myocardium, and the influence of residual stresses on the material response is illustrated by considering the extension and inflation of a thick-walled circular cylindrical tube.

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Authors and Affiliations

  1. University of Glasgow, Glasgow, UK

    Ray W. Ogden

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  1. Ray W. Ogden
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Correspondence to Ray W. Ogden .

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Editors and Affiliations

  1. Institute of Biomechanics, Graz University of Technology, Graz, Austria

    Gerhard A. Holzapfel

  2. School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom

    Ray W. Ogden

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Ogden, R.W. (2017). Nonlinear Continuum Mechanics and Modeling the Elasticity of Soft Biological Tissues with a Focus on Artery Walls. In: Holzapfel, G., Ogden, R. (eds) Biomechanics: Trends in Modeling and Simulation. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-41475-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-41475-1_3

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