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A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects

A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects
A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects
This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.
hyperelasticity, anisotropy, elasticity tensor, soft tissue, pdl, finite element
1025-5842
337-345
Limbert, Georges
a1b88cb4-c5d9-4c6e-b6c9-7f4c4aa1c2ec
Middleton, John
f17a8eb5-cc2e-42a4-9654-ae6376629cab
Laizans, Janis
1dc9c65d-958f-431d-a836-97d04c85df29
Dobelis, Modros
dcaa3e66-0aed-4608-b8fe-eacc371be522
Knets, Ivar
78c6c5ca-2d26-4580-b4f5-c7def2ad060c
Limbert, Georges
a1b88cb4-c5d9-4c6e-b6c9-7f4c4aa1c2ec
Middleton, John
f17a8eb5-cc2e-42a4-9654-ae6376629cab
Laizans, Janis
1dc9c65d-958f-431d-a836-97d04c85df29
Dobelis, Modros
dcaa3e66-0aed-4608-b8fe-eacc371be522
Knets, Ivar
78c6c5ca-2d26-4580-b4f5-c7def2ad060c

Limbert, Georges, Middleton, John, Laizans, Janis, Dobelis, Modros and Knets, Ivar (2003) A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects. Computer Methods in Biomechanics and Biomedical Engineering, 6 (5 & 6), 337-345. (doi:10.1080/10255840310001637572).

Record type: Article

Abstract

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.

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More information

Published date: October 2003
Keywords: hyperelasticity, anisotropy, elasticity tensor, soft tissue, pdl, finite element

Identifiers

Local EPrints ID: 68678
URI: http://eprints.soton.ac.uk/id/eprint/68678
ISSN: 1025-5842
PURE UUID: 74e4f6c2-cf2f-4f54-adc5-476c62ad59c3

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Date deposited: 16 Sep 2009
Last modified: 13 Mar 2024 19:03

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Contributors

Author: Georges Limbert
Author: John Middleton
Author: Janis Laizans
Author: Modros Dobelis
Author: Ivar Knets

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