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Visco-plasticity and plasticity an alternative for finite element solution of material nonlinearities

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Book cover Computing Methods in Applied Sciences and Engineering Part 1

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 10))

Abstract

In this paper, authors present a formulation and some computational details dealing with a general elastic/visco-plastic material where nonlinear elasticity is admissible and the flow rule and yield condition need not be associated.

If, in a visco-plastic solution method, stationary conditions are reached for the displacements, the solution to an equivalent plasticity problem is obtained. The visco-plastic approach thus provides an alternative technique to solve elasto-plastic problems, and which is found to possess considerable merits vis à vis other iterative processes.

In particular, non-associated flow rules and strain softening can be dealt with in a general purpose program without requiring specific numerical artifices. Further, by providing always an equilibrating solution (within the approximations of the finite element discretisation) and, at displacements stationarity, ensuring a plastically admissible stress distribution, results always give a lower bound to collapse.

The paper includes several examples to illustrate the application of the method to some problems of practical interest.

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Author information

Author notes

  1. I. C. Cormeau

    Present address: , Swansea

Authors and Affiliations

  1. University of Wales, Swansea

    O. C. Zienkiewicz (Professor of Civil Engineering)

  2. Aspirant F.N.R.S., Université Libre de Bruxelles, Belgium

    I. C. Cormeau

Authors
  1. O. C. Zienkiewicz
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  2. I. C. Cormeau
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R. Glowinski J. L. Lions

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© 1974 Springer-Verlag Berlin Heidelberg

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Zienkiewicz, O.C., Cormeau, I.C. (1974). Visco-plasticity and plasticity an alternative for finite element solution of material nonlinearities. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering Part 1. Lecture Notes in Computer Science, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015179

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  • DOI: https://doi.org/10.1007/BFb0015179

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06768-9

  • Online ISBN: 978-3-540-38374-1

  • eBook Packages: Springer Book Archive

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