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On the incremental solution of elasto-plastic continua in the range of large displacements

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Sommario

Si studia il problema della soluzione incrementale dei continui elasto-plastici in regime di grandi spostamenti e piccole deformazioni.

Si assume l'ipotesi di meccanismi multipli interagenti con leggi di flusso associate.

Viene definita una condizione sufficiente di unicità della soluzione incrementale e vengono forniti alcuni principi di minimo atti alla definizione numerica della detta soluzione.

Il lavoro viene concluso da alcune considerazioni in merito al problema della stabilità.

Summary

This paper studies the problem of incremental solution of elastoplastic continua in the case of large displacements and small strains.

Multiple interacting mechanisms under associated flow laws are assumed.

A sufficient condition of uniqueness of incremental solution is determined and some minimum principles are furnished for the numerical definition of said solution.

The problem of stability is discussed.

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References

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  5. O. De Donato,Extension to continua of some minimum theorems in elasto-plastic theory, Meccanica, 1968.

  6. M. Capurso,Principi di minimo per la soluzione incrementale dei problemi elasto-plastici, Nota I e II, Acc. Naz. Lincei, 1969.

  7. M. Capurso andG. Maier,Incremental elasto-plastic analysis and quadratic optimization, Meccanica, no 2, Vol. 5, 1970.

  8. R. Hill,A general theory of uniqueness and stability in elastic plastic solids, Jour. Mech. Phys. Solids, 1958.

  9. F. R. Shanley,Inelastic column theory, Jour. Aeronaut. Sci., 1947.

  10. H. J. Greenberg,On the variational principles of plasticity, Report All-S4, Grad. Div. Appl. Math., Brown University, 1949.

  11. D. C. Drucker,On the postulate of stability of material in the mechanics of continua, Jour. de Mec., 1964.

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Authors and Affiliations

  1. Istituto di Tecnica delle Costruzioni, Università di Napoli, Italy

    Michele Capurso

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  1. Michele Capurso
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Additional information

The results presented in this paper were obtained in the course of research sponsored by the C.N.R., “Gruppo Plasticità”.

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Capurso, M. On the incremental solution of elasto-plastic continua in the range of large displacements. Meccanica 5, 98–106 (1970). https://doi.org/10.1007/BF02134213

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  • DOI: https://doi.org/10.1007/BF02134213

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