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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 84
Determination of Constitutive Material Parameters for Sheet Metal Forming M. Kompis, T.G. Faurholdt, "Determination of Constitutive Material Parameters for Sheet Metal Forming", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 84, 2001. doi:10.4203/ccp.73.84
Keywords: inverse identification, optimization, finite element, deep drawing.Summary
This paper shows a method, which enables determination of material parameters
in advanced constitutive models in elasto-plastic strain range. The approach is based
on inverse method in which experimental methods, FE (finite element) simulations
and the optimization based on Levenberg-Marquardt technique[1] are employed.
Classical experimental tests (e.g. uniaxial tension test, bulge test or compression
tests) can be carried out only in limited strain range and therefore it is believed that
the data obtained from inverse method, which includes the whole stain range of
applied experiment, can be considered for better approximation of reality.
The inverse identification procedure is as follows: Experimental tests are carried out and the data are recorded, e.g. the force- displacement curve. The tests are also simulated using FE-software starting with some chosen material parameters. The material parameters and the friction coefficient are treated as unknowns in the optimization procedure. The objective function is build as a difference between the calculated and the measured punch force formulated in a least square sense. The parameters are then changed using optimization techniques until the objective function reaches a minimum. The values of the parameters at the minimum point are the searched parameters. In case of anisotropy a more complex objective function, which includes also geometric quantities, is implemented. Two identification problems based on deep drawing experiment are presented. In the first analysis the material is considered to be isotropic. Material parameters are identified using objective function expressed by:
where is experimentally determined punch force and is calculated punch force.
The drawing process is divided on
where is experimentally determined punch force and is calculated punch
force,
is experimentally determined flange diameter taken in direction ,
, or degrees to the rolling direction,
is calculated flange
diameter in direction , , or , degrees to the rolling direction.
The index is used to distinguish the three applied rolling directions.
The index is used to distinguish
three applied rolling directions. The drawing process is divided on References
- 1
- Arora, J. S., "Introduction to optimum design", McGraw-Hill Book Company, Singapore, 1989.
- 2
- Hosford W. F., Caddel M.C., "Metal forming", Prentice-Hall, 1993.
- 3
- Benchmark data from "Proceedings of NUMISHEET'99 Volume 2", Eds.: Gekin, J.C., Picart. P., University of Franche-Comte and ENSMM Besancon, France, 1999.
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