Computational Mechanics

, Volume 51, Issue 6, pp 949–959

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

Open AccessOriginal Paper

DOI: 10.1007/s00466-012-0775-x

Cite this article as:
Bednarek, T. & Kowalczyk, P. Comput Mech (2013) 51: 949. doi:10.1007/s00466-012-0775-x


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.


Contact modelingPenalty approachMetal formingDeep drawing
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© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland
  2. 2.Kazimierz Wielki UniversityBydgoszczPoland