First order finite element formulations for third medium contact

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. 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.

• 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: Str. 829–845
• Numbering: Vol. 76
• PID: 20.500.12556/RUL-180557
• UDC: 519.62:539.3
• ISSN on article: 0178-7675
• DOI: 10.1007/s00466-025-02628-y
• COBISS.SI-ID: 271228163
• Publication date in RUL: 11.03.2026

Record is a part of a journal

• Title: Computational mechanics
• Shortened title: Comput. mech.
• Publisher: Springer Nature
• ISSN: 0178-7675
• COBISS.SI-ID: 6668037

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