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Limit-analysis of a circular cylinder obeying the Green plasticity criterion and loaded in combined tension and torsion

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Abstract

This short paper presents the limit-analysis of a cylinder with circular basis, made of an ideal-plastic material obeying Green’s yield criterion and subjected to combined tension and torsion. The exact solution of the problem is provided in the form of a statically and plastically admissible stress field and a kinematically admissible velocity field, associated via the normality rule. The overall yield locus, that is the set of pairs [tension force, torsion torque] for which unrestrained plastic flow occurs, is expressed first in parametric form, then explicitly upon elimination of the parameter involved. The explicit expression of this yield locus also entails that of the overall flow rule via the overall normality property. The impact of these results is two-fold. First, they provide a fresh example of a solution to a limit-analysis problem exceptionally combining three generally mutually exclusive features: be non-trivial, exact and explicit. Second, they provide a way of using simple experiments of combined tension and torsion of cylinders to determine the parameter characterizing the influence of the mean stress in Green’s criterion.

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Notes

  1. Drucker et al. [6] have shown that when a structure made of some elastic-ideal-plastic material reaches a limit-load, the elastic strain rate is zero at all points of this structure, which means that it behaves as if its constitutive material were rigid-ideal-plastic.

  2. One may a priori envisage to perform even simpler experiments in pure tension; in theory \(\alpha \) could then be determined by comparing the axial and transverse strains. But accurate measurement of the transverse strain would be difficult.

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Acknowledgements

Jean-Baptiste Leblond acknowledges financial support by the Institut Universitaire de France under Grant éOTP L10K018.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences, Université de Lomé, Lomé, Togo

    Nadjime Pindra

  2. Sorbonne Université, Faculté des Sciences (formerly Université Pierre et Marie Curie), CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, Tour 65-55, 4 place Jussieu, 75252, Paris Cedex 05, France

    Jean-Baptiste Leblond & Djimédo Kondo

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  1. Nadjime Pindra
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  3. Djimédo Kondo
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Correspondence to Jean-Baptiste Leblond.

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Pindra, N., Leblond, JB. & Kondo, D. Limit-analysis of a circular cylinder obeying the Green plasticity criterion and loaded in combined tension and torsion. Meccanica 53, 2437–2446 (2018). https://doi.org/10.1007/s11012-018-0833-3

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