First order finite element formulations for third medium contact

authored by: P. Wriggers, J. Korelc, Ph Junker
Abstract: Third medium contact can be applied in situations where large deformations occur and self-contact is possible. This specific discretization technique has the advantage that the inequality constraint, inherent in contact formulations, is circumvented. The approach has several applications, like soft robotic or topology optimization. Recent approaches have been explored, using the gradient of the deformation measure to improve algorithmic performance. However, these methods typically require quadrilateral or hexahedral finite elements with quadratic shape functions, adding to their complexity. Also, the computation of second order gradients using quadratic triangular or tetrahedral elements does not lead to reasonable results since these gradients are constant at element level. In this paper, we apply a new regularization technique to triangular and tetrahedral finite elements of lowest ansatz order that approximates the gradient computations and thus reduces computational complexity.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Ljubljana
Type: Article
Journal: Computational mechanics
ISSN: 0178-7675
Publication date: 2025
Publication status: Accepted/In press
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-025-02628-y (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{42f359607a81434688a0620c0bfcdfe2,
title = "First order finite element formulations for third medium contact",
abstract = "Third medium contact can be applied in situations where large deformations occur and self-contact is possible. This specific discretization technique has the advantage that the inequality constraint, inherent in contact formulations, is circumvented. The approach has several applications, like soft robotic or topology optimization. Recent approaches have been explored, using the gradient of the deformation measure to improve algorithmic performance. However, these methods typically require quadrilateral or hexahedral finite elements with quadratic shape functions, adding to their complexity. Also, the computation of second order gradients using quadratic triangular or tetrahedral elements does not lead to reasonable results since these gradients are constant at element level. In this paper, we apply a new regularization technique to triangular and tetrahedral finite elements of lowest ansatz order that approximates the gradient computations and thus reduces computational complexity.",
keywords = "Finite deformations, Finite elements, Frictionless contact, Hyperelasticity",
author = "P. Wriggers and J. Korelc and Ph Junker",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",
year = "2025",
doi = "10.1007/s00466-025-02628-y",
language = "English",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
}