A third medium approach for contact using first and second order finite elements

Wriggers, Peter (author), Korelc, Jože (author), Junker, Ph. (author)

Third medium contact can be applied in situations where large deformations occur and self-contact is possible. Starting with Wriggers et al. (2013), this approach has been further developed and often applied in the area of topology optimization. Lately approaches have been discussed which use the gradient of the deformation measure to enhance the performance of the algorithm. Such approaches, however, require finite elements with quadratic shape function. In this paper two new regularization techniques are introduced which on one hand reduce the complexity of the gradient computation of the deformation measure and on the other hand allow the use of finite elements with linear shape functions. The approaches will be critically evaluated and applied to different two-dimensional problems.

• Language: English
• Keywords: frictionless contact, finite deformations, finite elements, hyperelasticity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 16 str.
• Numbering: Vol. 436, art. 117740
• PID: 20.500.12556/RUL-180555
• UDC: 519.62:539.3
• ISSN on article: 1879-2138
• DOI: 10.1016/j.cma.2025.117740
• COBISS.SI-ID: 271211267
• Publication date in RUL: 11.03.2026

Record is a part of a journal

• Title: Computer Methods in Applied Mechanics and Engineering
• Publisher: Elsevier
• ISSN: 1879-2138
• COBISS.SI-ID: 22956805

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kontaktni problemi, velike deformacije, končni elementi, hiperelastičnost

Projects

• Funder: Other - Other funder or multiple funders
• Funding programme: Deutsche Forschungsgemeinschaft
• Project number: 390833453
• Name: PhoenixD: Photonics, Optics, and Engineering – Innovation Across Disciplines

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0158
• Name: Gradbene konstrukcije in gradbena fizika