Nonlinear continuum mechanics and modelling the elasticity of soft biological tissues with a focus on artery walls

Ogden, R. W. (2017) Nonlinear continuum mechanics and modelling the elasticity of soft biological tissues with a focus on artery walls. In: Holzapfel, G. A. and Ogden, R. W. (eds.) Biomechanics: Trends in Modeling and Simulation. Series: Studies in Mechanobiology, Tissue Engineering and Biomaterials (20). Springer International Publishing, pp. 83-156. ISBN 9783319414737 (doi:10.1007/978-3-319-41475-1_3)

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Publisher's URL: http://www.springer.com/gb/book/9783319414737

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.

Item Type:Book Sections
Status:Published
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Ogden, R. W.
Subjects:Q Science > Q Science (General)
Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Publisher:Springer International Publishing
ISBN:9783319414737
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