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Objective stress rates in repeated elastic deformation cycles
Author(s) -
Meyers Albert,
Bruhns Otto,
Xiao Heng
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510101
Subject(s) - deformation (meteorology) , eulerian path , simple (philosophy) , stress (linguistics) , isotropy , mathematics , logarithm , mathematical analysis , mechanics , materials science , physics , composite material , philosophy , linguistics , epistemology , lagrangian , quantum mechanics
The Eulerian elastoplastic description of initially isotropic materials essentially depends on the accurate formulation of the elastic deformation. This is often represented by Truesdell's hypoelastic equation, which involves an objective stress rate. Many objective stress rates have been presented in the past. With Bernstein's integrability conditions it has been shown that only a particular rate, namely the logarithmic stress rate, makes the hypoelastic relation exactly integrable. Here, we propose a simple, one‐parameter closed deformation cycle to demonstrate the error which will considerably accumulate over several cycles, whenever a non‐appropriate stress rate is in use. For this, several objective stress rates are compared in this cycle and the residual stresses at the end of the cycles are examined. By such a simple procedure the mathematical results of non‐integrability are evidenced by example. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)