Improvement of stability conditions, accuracy and uniqueness of penalty approach in contact modeling
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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.
KeywordsContact modeling Penalty approach Metal forming Deep drawing
This study was partially financed by European Regional Development Fund within the framework of the Innovative Economy Programme, Project Number POIG.01.03.01-14-209/09.
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
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