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Title: The von Mises model vor one-dimensional elastoplastic beams and Prandtl-Ishlinskii hysteresis operators
Authors: Krejčí, PavelSprekels, Jürgen
Issue Date: 2006
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1143, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: In this paper, the one-dimensional equation for the transversal vibrations of an elastoplastic beam is derived from a general three-dimensional system. The plastic behavior is modeled using the classical three-dimensional von Mises plasticity model. It turns out that this single-yield model without hardening leads after a dimensional reduction to a multi-yield one-dimensional hysteresis model with kinematic hardening, given by a hysteresis operator of Prandtl-Ishlinskii type whose density function can be determined explicitly. This result indicates that the use of Prandtl-Ishlinskii hysteresis operators in the modeling of elastoplasticity is not just a questionable phenomenological approach, but in fact quite natural. In addition to the derivation of the model, it is shown that the resulting partial differential equation with hysteresis can be transformed into an equivalent system for which the existence and uniqueness of a strong solution is proved. The proof employs techniques from the mathematical theory of hysteresis operators.
Keywords: Elastoplasticity; beam equation; hysteresis operators; Prandtl-Ishlinskii model; von Mises model
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
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