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A mortar finite element approach for point, line, and surface contact
Author(s) -
Farah P.,
Wall W. A.,
Popp A.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5743
Subject(s) - lagrange multiplier , finite element method , discretization , mortar methods , penalty method , mathematics , robustness (evolution) , mathematical analysis , mixed finite element method , mathematical optimization , structural engineering , engineering , gene , biochemistry , chemistry
Summary An approach for investigating finite deformation contact problems with frictional effects with a special emphasis on nonsmooth geometries such as sharp corners and edges is proposed in this contribution. The contact conditions are separately enforced for point contact, line contact, and surface contact by employing 3 different sets of Lagrange multipliers and, as far as possible, a variationally consistent discretization approach based on mortar finite element methods. The discrete unknowns due to the Lagrange multiplier approach are eliminated from the system of equations by employing so‐called dual or biorthogonal shape functions. For the combined algorithm, no transition parameters are required, and the decision between point contact, line contact, and surface contact is implicitly made by the variationally consistent framework. The algorithm is supported by a penalty regularization for the special scenario of nonparallel edge‐to‐edge contact. The robustness and applicability of the proposed algorithms are demonstrated with several numerical examples.