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

• Published in: Acta mechanica 2020-04, Vol.231 (4), p.1519-1538
• Main Authors: Obrezkov, Leonid P., Matikainen, Marko K., Harish, Ajay B.
• Format: Article
• Language: English
• Subjects: Anisotropy; Biological models (mathematics); Classical and Continuum Physics; Comparative analysis; Computational fluid dynamics; Control; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Heat and Mass Transfer; Original Paper; Rubber; Soft tissues; Software; Solid Mechanics; Theoretical and Applied Mechanics; Three dimensional models; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-019-02607-4

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.