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A rotation-based approach to third medium contact regularization

Dahlberg, Vilmer LU ; Sjövall, Filip LU orcid ; Dalklint, Anna LU and Wallin, Mathias LU (2026) In Computer Methods in Applied Mechanics and Engineering 453.
Abstract

The third medium contact method utilizes a fictitious “third” medium to implicitly model contact interactions. When contact occurs, the fictitious medium is severely deformed which necessitates numerical regularization to ensure numerical stability. Ultimately, this regularization should promote good element quality but otherwise not interfere with the modeling of the contact mechanics. One approach penalizes both stretch and rotational deformation modes using the displacement Hessian which requires higher order elements. Another approach introduces additional degrees of freedom to penalize an approximation of the rotation gradient which drastically increases the system size. We propose a new regularization based on an approximation of... (More)

The third medium contact method utilizes a fictitious “third” medium to implicitly model contact interactions. When contact occurs, the fictitious medium is severely deformed which necessitates numerical regularization to ensure numerical stability. Ultimately, this regularization should promote good element quality but otherwise not interfere with the modeling of the contact mechanics. One approach penalizes both stretch and rotational deformation modes using the displacement Hessian which requires higher order elements. Another approach introduces additional degrees of freedom to penalize an approximation of the rotation gradient which drastically increases the system size. We propose a new regularization based on an approximation of the rotation gradient in the fictitious medium, which does not penalize stretch deformation modes and can be used with first-order elements. The efficacy of our method is exemplified using several numerical examples including benchmark tests, an investigation of parasitic forces in the third medium and a novel application to general loading condition.

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Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Contact, Metric, Rotation, Third Medium Contact
in
Computer Methods in Applied Mechanics and Engineering
volume
453
article number
118801
publisher
Elsevier
external identifiers
  • scopus:105029744833
ISSN
0045-7825
DOI
10.1016/j.cma.2026.118801
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2026 The Author(s)
id
a4ee148b-ec4b-4cca-bcc6-ba3ad81f4ab0
date added to LUP
2026-08-07 13:07:07
date last changed
2026-08-11 14:48:37
@article{a4ee148b-ec4b-4cca-bcc6-ba3ad81f4ab0,
  abstract     = {{<p>The third medium contact method utilizes a fictitious “third” medium to implicitly model contact interactions. When contact occurs, the fictitious medium is severely deformed which necessitates numerical regularization to ensure numerical stability. Ultimately, this regularization should promote good element quality but otherwise not interfere with the modeling of the contact mechanics. One approach penalizes both stretch and rotational deformation modes using the displacement Hessian which requires higher order elements. Another approach introduces additional degrees of freedom to penalize an approximation of the rotation gradient which drastically increases the system size. We propose a new regularization based on an approximation of the rotation gradient in the fictitious medium, which does not penalize stretch deformation modes and can be used with first-order elements. The efficacy of our method is exemplified using several numerical examples including benchmark tests, an investigation of parasitic forces in the third medium and a novel application to general loading condition.</p>}},
  author       = {{Dahlberg, Vilmer and Sjövall, Filip and Dalklint, Anna and Wallin, Mathias}},
  issn         = {{0045-7825}},
  keywords     = {{Contact; Metric; Rotation; Third Medium Contact}},
  language     = {{eng}},
  month        = {{05}},
  publisher    = {{Elsevier}},
  series       = {{Computer Methods in Applied Mechanics and Engineering}},
  title        = {{A rotation-based approach to third medium contact regularization}},
  url          = {{http://dx.doi.org/10.1016/j.cma.2026.118801}},
  doi          = {{10.1016/j.cma.2026.118801}},
  volume       = {{453}},
  year         = {{2026}},
}