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Higher-Order Mesoscopic Theories of Plasticity Based on Discrete Dislocation Interactions

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Mechanics of Generalized Continua

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 21))

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Abstract

In this chapter, a rigorous analysis is given as a reference in which dislocations are treated as discrete entities. Then the transition towards a crystalline continuum is made in a number of steps by subsequent averaging along and perpendicular to the slip direction. This procedure eliminates the short-range dislocation interactions. Based on the considered idealized configuration, a back-stress term is derived which allows the conventional theory to predict finite-size pile-ups and turns out to be virtually identical to the result obtained by means of statistical arguments.

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References

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  5. Kasyanyuk, Y., Peerlings, R.H.J., Geers, M.G.D.: In preparation

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  6. Roy, A., Peerlings, R.H.J., Geers, M.G.D., Kasyanyuk, Y.: Continuum modelling of dislocation interactions: Why discreteness matters? Mater. Sci. Eng. A 486, 653–661 (2008)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands

    Robert H. J. Peerlings, Y. Kasyanyuk, A. Roy & M. G. D. Geers

Authors
  1. Robert H. J. Peerlings
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  2. Y. Kasyanyuk
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  3. A. Roy
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  4. M. G. D. Geers
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Corresponding author

Correspondence to Robert H. J. Peerlings .

Editor information

Editors and Affiliations

  1. Institut Jean Le Rond d'Alembert, Université Paris VI, place Jussieu 4, Paris CX 5, 75252, France

    Gérard A. Maugin

  2. Faculty of Civil Engineering and, Delft University of Technology,, Stevinweg 1, Delft, 2628 CN, Netherlands

    Andrei V. Metrikine

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Peerlings, R.H.J., Kasyanyuk, Y., Roy, A., Geers, M.G.D. (2010). Higher-Order Mesoscopic Theories of Plasticity Based on Discrete Dislocation Interactions. In: Maugin, G., Metrikine, A. (eds) Mechanics of Generalized Continua. Advances in Mechanics and Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5695-8_25

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