Abstract
A review of principal results concerning the quasi-static response of an elastic- plastic or elastic-viscoplastic structure undergoing infinitesimal transformation is given. It is concerned principally with the perfect plastic model and with a straightforward generalization denoted as the generalized standard model Both of these models are based upon the classical assumptions of normality and convexity. Firstly, the rate problem is recalled and associated minimum principles are formulated. Secondly, a global description of the evolution is introduced and global results are derived such as uniqueness and existence theorems. Elastic and plastic shake-down theorems are then presented from an asymptotic analysis of the response of the structure under cyclic or periodic loading.
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© 1986 Elsevier Applied Science Publishers Ltd
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Son, N.Q. (1986). Basic Theorems of Elastoplasticity. In: Gittus, J., Zarka, J. (eds) Modelling Small Deformations of Polycrystals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4181-6_3
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DOI: https://doi.org/10.1007/978-94-009-4181-6_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8357-7
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