TY - JOUR
T1 - An exponential constitutive model excluding fibres under compression
T2 - Application to extension–inflation of a residually stressed carotid artery
AU - Li, Kewei
AU - Ogden, Ray W.
AU - Holzapfel, Gerhard A.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - 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.
AB - 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.
KW - carotid artery
KW - Constitutive modelling
KW - exclusion of compressed fibres
KW - fibre dispersion
KW - residual stress
UR - http://www.scopus.com/inward/record.url?scp=85025598934&partnerID=8YFLogxK
U2 - 10.1177/1081286517712077
DO - 10.1177/1081286517712077
M3 - Article
AN - SCOPUS:85025598934
SN - 1081-2865
VL - 23
SP - 1206
EP - 1224
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
IS - 8
ER -