Derivation of strain-gradient plasticity from a generalized Peierls–Nabarro model

  • Sergio Conti

    Universität Bonn, Germany
  • Adriana Garroni

    Università di Roma, Italy
  • Stefan Müller

    Univeristät Bonn, Germany
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Abstract

We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in a plane. After scaling, from the nonlocal elastic interaction we derive a continuous energy with linear growth depending on a measure which characterizes the macroscopic dislocation density as well as a nonlocal effective energy representing the far-field interaction between dislocations. Relaxation and formation of microstructures at intermediate scales are automatically incorporated in the limiting procedure based on -convergence.

Cite this article

Sergio Conti, Adriana Garroni, Stefan Müller, Derivation of strain-gradient plasticity from a generalized Peierls–Nabarro model. J. Eur. Math. Soc. 25 (2023), no. 7, pp. 2487–2524

DOI 10.4171/JEMS/1242