Li, K., Ogden, R. W. and Holzapfel, G. A. (2018) An exponential constitutive model excluding fibers under compression: application to extension-inflation of a residually stressed carotid artery. Mathematics and Mechanics of Solids, 23(8), pp. 1206-1224. (doi: 10.1177/1081286517712077)
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Abstract
Detailed information on the three-dimensional dispersion of collagen fibres within layers of healthy and diseased soft biological tissues has been reported recently. Previously we have proposed a constitutive model for soft fibrous solids based on the angular integration approach which allows the exclusion of any compressed collagen fibre within the dispersion. In addition, a computational implementation of that model in a general purpose finite element program has been investigated and verified with the standard fibre-reinforcing model for fibre contributions. In this study, we develop the proposed fibre dispersion model further using an exponential form of the strain-energy function for the fibre contributions. The finite element implementation of this model with a rotationally symmetrical dispersion of fibres is also presented. This includes explicit expressions for the stress and elasticity tensors. The performance and implementation of the new model are demonstrated by means of a uniaxial extension test, a simple shear test, and an extension–inflation simulation of a residually stressed carotid artery segment. In each example we have obtained good agreement between the finite element solution and the analytical or experimental results.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Ogden, Professor Raymond and Holzapfel, Professor Gerhard |
| Authors: | Li, K., Ogden, R. W., and Holzapfel, G. A. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Mathematics and Mechanics of Solids |
| Journal Abbr.: | MMS |
| Publisher: | SAGE Publications |
| ISSN: | 1081-2865 |
| ISSN (Online): | 1741-3028 |
| Published Online: | 16 June 2017 |
| Copyright Holders: | Copyright © 2017 The Authors |
| First Published: | First published in Mathematics and Mechanics of Solids 23(8):1206-1224 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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