A finite element for soft tissue deformation based on the absolute nodal coordinate formulation

authored by: Leonid P. Obrezkov, Marko K. Matikainen, Ajay B. Harish
Abstract: This paper introduces an implementation of the absolute nodal coordinate formulation (ANCF) that can be used to model fibrous soft tissue in cases of three-dimensional elasticity. It is validated against results from existing incompressible material models. The numerical results for large deformations based on this new ANCF element are compared to results from analytical and commercial software solutions, and the relevance of the implementation to the modeling of biological tissues is discussed. Also considered is how these results relate to the classical results seen in Treloar’s rubber experiments. All the models investigated are considered from both elastic and static points of view. For isotropic cases, neo-Hookean and Mooney–Rivlin models are examined. For the anisotropic case, the Gasser–Ogden–Holzapfel model, including a fiber dispersion variation, is considered. The results produced by the subject ANCF models agreed with results obtained from the commercial software. For the isotropic cases, in fact, the numerical solutions based on the ANCF element were more accurate than those produced by ANSYS.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Lappeenranta University of Technology (LUT)
Type: Article
Journal: Acta mechanica
Volume: 231
Pages: 1519-1538
No. of pages: 20
ISSN: 0001-5970
Publication date: 01.04.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanical Engineering
Electronic version(s): https://doi.org/10.1007/s00707-019-02607-4 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{dfbe5a3591484412a7b6b22c83e0d94d,
title = "A finite element for soft tissue deformation based on the absolute nodal coordinate formulation",
abstract = "This paper introduces an implementation of the absolute nodal coordinate formulation (ANCF) that can be used to model fibrous soft tissue in cases of three-dimensional elasticity. It is validated against results from existing incompressible material models. The numerical results for large deformations based on this new ANCF element are compared to results from analytical and commercial software solutions, and the relevance of the implementation to the modeling of biological tissues is discussed. Also considered is how these results relate to the classical results seen in Treloar{\textquoteright}s rubber experiments. All the models investigated are considered from both elastic and static points of view. For isotropic cases, neo-Hookean and Mooney–Rivlin models are examined. For the anisotropic case, the Gasser–Ogden–Holzapfel model, including a fiber dispersion variation, is considered. The results produced by the subject ANCF models agreed with results obtained from the commercial software. For the isotropic cases, in fact, the numerical solutions based on the ANCF element were more accurate than those produced by ANSYS.",
author = "Obrezkov, {Leonid P.} and Matikainen, {Marko K.} and Harish, {Ajay B.}",
note = "Funding Information: We would like to thank the Research Foundation of the Lappeenranta University of Technology and the Academy of Finland (Application No. 299033 for funding 519 of Academy Research Fellow) for the generous grants that made this work possible. ",
year = "2020",
month = apr,
day = "1",
doi = "10.1007/s00707-019-02607-4",
language = "English",
volume = "231",
pages = "1519--1538",
journal = "Acta mechanica",
issn = "0001-5970",
publisher = "Springer-Verlag Wien",
number = "4",
}