Automation of finite element formulations for large deformation contact problems

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 act...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2011-03, Vol.85 (10), p.1252-1279
Main Authors: Lengiewicz, Jakub, Korelc, Jože, Stupkiewicz, Stanisław
Format: Article
Language:English
Subjects:
augmented Lagrangian method
automatic differentiation
Automation
Computational efficiency
Contact
contact smoothing
Deformation
Exact sciences and technology
Finite element method
frictional contact
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Mechanical contact (friction...)
Physics
Solid mechanics
Structural and continuum mechanics
symbolic methods
Three dimensional
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Summary: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 © 2010 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.3009