An exponential constitutive model excluding fibers under compression: application to extension-inflation of a residually stressed carotid artery

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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