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Singular Solutions in Plane Strain Plasticity

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Encyclopedia of Continuum Mechanics

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Synonyms

Asymptotic analysis; Double-shearing model; Infinite strain rate; Maximum friction law; Maximum friction surface; Rigid perfectly plastic model; Rigid plastic models; Strain rate intensity factor; Viscoplastic model

Definitions

  1. 1.

    The maximum friction law demands that the friction stress is equal to the shear yield stress in the case of pressure-independent models considered,

  2. 2.

    The maximum friction law demands that the friction surface coincides with a stress characteristic or an envelope of stress characteristics in the case of the double-shearing model,

  3. 3.

    The maximum friction surface is a surface with maximum friction,

  4. 4.

    The strain rate intensity factor is the coefficient of the leading term in a series expansion of the quadratic invariant of the strain rate tensor in the vicinity of maximum friction surfaces.

The definition for the maximum friction law above applies at sliding.

Introduction

The successful mathematical modelling of the material behavior in the vicinity of...

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References

  • Alexandrov S, Harris D (2006) Comparison of solution behaviour for three models of pressure-dependent plasticity: a simple analytical example. Int J Mech Sci 48(7):750–762

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Acknowledgements

This work was made possible by grant 17-01-00624 from RFBR (Russia).

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    Sergei Alexandrov

Authors
  1. Sergei Alexandrov
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Corresponding author

Correspondence to Sergei Alexandrov .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    Sergey Alexandrov

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Alexandrov, S. (2019). Singular Solutions in Plane Strain Plasticity. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_367-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_367-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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