Bending of an elastoplastic strip with isotropic and kinematic hardening |
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Authors: | O T Bruhns N K Gupta A T M Meyers H Xiao |
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Institution: | (1) Institute of Mechanics, Ruhr-University Bochum, D-44780 Bochum, Germany e-mail: bruhns@tm.bi.ruhr-uni-bochum.de, DE;(2) Department of Applied Mechanics, Indian Institute of Technology, New Delhi 110016, India, IN |
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Abstract: | Summary We propose an exact analysis for finite bending of a compressible elastoplastic strip with combined hardening at a given
stretch normal to the bending plane. We apply the self-consistent eulerian rate-type elastoplastic model based on the logarithmic
rate, in conjunction with a Tresca-type loading function. Utilizing the maximum circumferential stretch at the outer surface
as an independent parameter, we derive exact analytic expressions for the bending angle, the bending moment, the outer and
inner radii, the radii of the two elastic-plastic interfaces and the circumferential stretches at these two interfaces, as
well as the stress distributions in every current cross section. In particular, we establish an explicit relation between
the two circumferential stretches at the two elastic-plastic interfaces, and we show that this relation is universal for all
cases of hardening. We show also that the maximum and minimum circumferential stretches at the outer and inner surfaces obey
a reciprocal relation in the course of both elastic and elastic-plastic deformations.
Received 4 June 2002; accepted for publication 14 November 2002
This research was carried out under financial support from the German Science Foundation (DFG) (Contract No.: Br. 580/26-2)
and from Alexander von Humboldt Foundation. We wish to express our sincere gratitude to these Foundations. |
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Keywords: | Finite Strain Elastoplasticity Hardening Strip Bending Rate-type Model |
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