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A Variational Model for Dislocations at Semi-coherent Interfaces

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Abstract

We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations and a bulk elastic energy, spent to decrease the amount of dislocations needed to compensate the lattice misfit. We prove that, for minimizers, the former scales like the surface area of the interface, the latter like its diameter. The proposed continuum model is built on some explicit computations done in the framework of the semi-discrete theory of dislocations. Even if we deal with finite elasticity, linearized elasticity naturally emerges in our analysis since the far-field strain vanishes as the interface size increases.

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Authors and Affiliations

  1. Department of Mathematics, University of Sussex, Pevensey 2 Building, Falmer Campus, Brighton, BN1 9QH, UK

    Silvio Fanzon & Mariapia Palombaro

  2. Dipartimento di Matematica, Sapienza Università di Roma, 00185, Rome, Italy

    Marcello Ponsiglione

Authors
  1. Silvio Fanzon
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  2. Mariapia Palombaro
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  3. Marcello Ponsiglione
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Correspondence to Marcello Ponsiglione.

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Communicated by Irene Fonseca.

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Fanzon, S., Palombaro, M. & Ponsiglione, M. A Variational Model for Dislocations at Semi-coherent Interfaces. J Nonlinear Sci 27, 1435–1461 (2017). https://doi.org/10.1007/s00332-017-9366-5

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  • DOI: https://doi.org/10.1007/s00332-017-9366-5

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