An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery

Research output: Contribution to journalArticleResearchpeer-review

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.

LanguageEnglish
Pages1206-1224
Number of pages19
JournalMathematics and mechanics of solids
Volume23
Issue number8
DOIs
StatusPublished - 1 Aug 2018

Fingerprint

Exponential Model
Arteries
Constitutive Model
Constitutive models
Inflation
Compaction
Compression
Fiber
Fibers
Collagen
Finite Element
Biological Tissue
Model
Strain Energy
Finite Element Solution
Strain energy
Energy Function
Tensors
Elasticity
Tensor

Keywords

  • carotid artery
  • Constitutive modelling
  • exclusion of compressed fibres
  • fibre dispersion
  • residual stress

ASJC Scopus subject areas

  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials

Cite this

An exponential constitutive model excluding fibres under compression : Application to extension–inflation of a residually stressed carotid artery. / Li, Kewei; Ogden, Ray W.; Holzapfel, Gerhard A.

In: Mathematics and mechanics of solids, Vol. 23, No. 8, 01.08.2018, p. 1206-1224.

Research output: Contribution to journalArticleResearchpeer-review

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