Improvement of stability conditions and uniqueness of penalty approach in contact modelling in sheet metal forming

Tomasz Bednarek^1,2, Piotr Kowalczyk¹, Artur Marczewski¹, Włodzimierz Sosnowski¹

¹Institute of Fundamental Technological Research of the Polish Academy of Sciences, 02-106 Warsaw, Pawinskiego 5B, Poland.
²Kazimierz Wielki University, 85-064 Bydgoszcz, Chodkiewicza 30, Poland.

DOI:

https://doi.org/10.7494/cmms.2011.2.0362

Abstract:

The main objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with viscoplastic and plastic material models. In this paper, the problem of convergence and uniqueness of the problem of non-linear simulation of sheet metal forming processes modeled using rigid-viscoplastic material model is considered. In the numerical simulation of the deformation process MFP2D and MFP3D Finite Element programs were used. The simplicity of the algorithm is the main advantage of these codes, the Direct Differentiation method and optimization modules can be implemented in the source code. The numerical instability caused by high values of the condition number of the main system of equations is the main disadvantage of the codes. The penalty approach contact model used in the program makes the stiffness matrix condition number worse.

Cite as:

Bednarek, T., Kowalczyk, P., Marczewski, A., & Sosnowski, W. (2011). Improvement of stability conditions and uniqueness of penalty approach in contact modelling in sheet metal forming. Computer Methods in Materials Science, 11(2), 411 – 417. https://doi.org/10.7494/cmms.2011.2.0362

Article (PDF):