Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 85, Issue 10, Pages 1252-1279Publisher
WILEY-BLACKWELL PUBLISHING, INC
DOI: 10.1002/nme.3009
Keywords
automatic differentiation; symbolic methods; automation; frictional contact; contact smoothing; augmented Lagrangian method
Funding
- Polish Ministry of Science and Higher Education [POIG.01.03.01-14-013/08-00]
- Polish-Slovenian bilateral cooperation programme
- KomCerMet project
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The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automatic-differentiation-based notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Copyright (C) 2010 John Wiley & Sons, Ltd.
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