Stability and uniqueness of flow approach algorithms in sheet metal forming simulations

Włodzimierz Sosnowski^1,2, Tomasz Bednarek^1,2, Piotr Kowalczyk¹

¹Institute of Fundamental Technological Research PAN, Warsaw, ul. Pawińskiego 5b.
²Kazimierz Wielki University, Bydgoszcz, ul. Chodkiewicza 30.

DOI:

https://doi.org/10.7494/cmms.2010.1.0274

Abstract:

The objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with rigid-viscoplastic and plastic material models. Two numerical codes, MFP2D and MFP3D, were used previously for practical industrial solutions (Sosnowski, 2001, Sosnowski, 1995, Sosnowski et al., 1992). Relative simplicity of both the codes allowed to include “exact” sensitivity calculations by direct differentiation method. This made it possible to perform very effective optimization of the whole sheet metal forming process simulation. One of significant drawbacks of rigid-viscoplastic shell approach is poor stability and convergence due to relatively high values of the condition number of the resulting system of equations. The reasons include the absence of elasticity terms in the constitutive material law and asymptotic character of the relationship between viscosity and effective plastic strain rate. Approximate character of the contact modeling (penalty approach) also affects conditioning of the system. This drawback can be overcome by some measures proposed in this paper.

Cite as:

Sosnowski, W., Bednarek, T., & Kowalczyk, P. (2010). Stability and uniqueness of flow approach algorithms in sheet metal forming simulations. Computer Methods in Materials Science, 10(1), 30-36. https://doi.org/10.7494/cmms.2010.1.0274

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