Improvement of stability conditions, accuracy and uniqueness of penalty approach in contact modeling

The main objective of this paper is to improve stability conditions, uniqueness and convergence of numerical analysis of metal forming processes with contact constraints enforced by the penalty method. A commonly known drawback of this approach is the choice of penalty factor values. When assumed to...

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Bibliographic Details
Published in:Computational mechanics 2013-06, Vol.51 (6), p.949-959
Main Authors: Bednarek, Tomasz, Kowalczyk, Piotr
Format: Article
Language:English
Subjects:
Adaptive algorithms
Adaptive systems
Algorithms
Analysis
Classical and Continuum Physics
Computational Science and Engineering
Contact
Engineering
Finite element method
Forming
Ill-conditioned problems (mathematics)
Mathematical analysis
Mathematical models
Metal forming
Metal sheets
Methods
Numerical analysis
Original Paper
Stability
Stability analysis
Theoretical and Applied Mechanics
Ultrasonic testing
Uniqueness
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Summary:The main objective of this paper is to improve stability conditions, uniqueness and convergence of numerical analysis of metal forming processes with contact constraints enforced by the penalty method. A commonly known drawback of this approach is the choice of penalty factor values. When assumed too low, they result in inaccurate fulfillment of the constraints while when assumed too high, they lead to ill-conditioning of the equations system which affects stability and uniqueness of the solution. The proposed modification of the penalty algorithm consists in adaptive estimation of the penalty factor values for the particular system of finite element equations and for the assumed allowed inaccuracy in fulfillment of the contact constraints. The algorithm is tested on realistic examples of sheet metal forming. The finite element code based on flow approach formulation (for rigid-plastic and rigid-viscoplastic material model) has been used.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-012-0775-x