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A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects.
Comput Methods Biomech Biomed Engin. 2003 Oct-Dec; 6(5-6):337-45.CM

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.

Authors+Show Affiliations

Biomechanics Research Unit, The Cardiff Medicentre, UWCM, Cardiff C 4UJ, UK. limbertg@cardiff.ac.ukNo affiliation info availableNo affiliation info availableNo affiliation info availableNo affiliation info available

Pub Type(s)

Comparative Study
Evaluation Study
Journal Article
Research Support, Non-U.S. Gov't
Validation Study

Language

eng

PubMed ID

14675954

Citation

Limbert, Georges, et al. "A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects." Computer Methods in Biomechanics and Biomedical Engineering, vol. 6, no. 5-6, 2003, pp. 337-45.
Limbert G, Middleton J, Laizans J, et al. A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects. Comput Methods Biomech Biomed Engin. 2003;6(5-6):337-45.
Limbert, G., Middleton, J., Laizans, J., Dobelis, M., & Knets, I. (2003). A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects. Computer Methods in Biomechanics and Biomedical Engineering, 6(5-6), 337-45.
Limbert G, et al. A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects. Comput Methods Biomech Biomed Engin. 2003 Oct-Dec;6(5-6):337-45. PubMed PMID: 14675954.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects. AU - Limbert,Georges, AU - Middleton,John, AU - Laizans,Janis, AU - Dobelis,Modris, AU - Knets,Ivar, PY - 2003/12/17/pubmed PY - 2004/8/25/medline PY - 2003/12/17/entrez SP - 337 EP - 45 JF - Computer methods in biomechanics and biomedical engineering JO - Comput Methods Biomech Biomed Engin VL - 6 IS - 5-6 N2 - 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. SN - 1025-5842 UR - https://www.unboundmedicine.com/medline/citation/14675954/A_transversely_isotropic_hyperelastic_constitutive_model_of_the_PDL__Analytical_and_computational_aspects_ L2 - http://www.tandfonline.com/doi/full/10.1080/10255840310001637572 DB - PRIME DP - Unbound Medicine ER -