A mortar-based frictional contact formulation for large deformations using Lagrange multipliers

authored by: M. Tur, F. J. Fuenmayor, Peter Wriggers
Abstract: In this work a Lagrange multiplier method is proposed to solve 2D Coulomb frictional contact problems in the context of large deformations. As the proposed formulation is based on the mortar method, the constraints are imposed in a weak integral sense along the contact surface. In order to compute the contact integrals, we use a numerical integration based on the definition of the kinematical variables (gap, slip and their variations) at the quadrature points. The linearization of non-linear equations (virtual work and contact constraints) is developed in order to apply a Newton's method. The examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Polytechnic University of Valencia
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 198
Pages: 2860-2873
No. of pages: 14
ISSN: 0045-7825
Publication date: 23.07.2009
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2009.04.007 (Access: Unknown)

BibTeX

@article{75254105281c4bc789c3dd70edfe421e,
title = "A mortar-based frictional contact formulation for large deformations using Lagrange multipliers",
abstract = "In this work a Lagrange multiplier method is proposed to solve 2D Coulomb frictional contact problems in the context of large deformations. As the proposed formulation is based on the mortar method, the constraints are imposed in a weak integral sense along the contact surface. In order to compute the contact integrals, we use a numerical integration based on the definition of the kinematical variables (gap, slip and their variations) at the quadrature points. The linearization of non-linear equations (virtual work and contact constraints) is developed in order to apply a Newton's method. The examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution.",
keywords = "Contact, Friction, Lagrange multiplier, Large sliding, Mortar method",
author = "M. Tur and Fuenmayor, {F. J.} and Peter Wriggers",
note = "Funding information: The authors wish to express their gratitude for the financial support received from the Spanish Ministry for Science and Technology under project DPI2007-66995-C03-02 and Universidad Politecnica de Valencia (PAID-06-09).",
year = "2009",
month = jul,
day = "23",
doi = "10.1016/j.cma.2009.04.007",
language = "English",
volume = "198",
pages = "2860--2873",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
number = "37-40",
}