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

  • Leonid P. Obrezkov
  • Marko K. Matikainen
  • Ajay B. HarishEmail author
Original Paper


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.



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.


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© Springer-Verlag GmbH Austria, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Lappeenranta University of TechnologyLappeenrantaFinland
  2. 2.Institute of Continuum MechanicsLeibniz University HannoverHannoverGermany

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