{
  "abstract": "A Fast Fourier Transform (FFT)-based micromechanical method for static Field Dislocation Mechanics (FDM) within a first Strain Gradient Elasticity (SGE) theory of Mindlin-type is developed. The kinematics equations of dislocation defects are first presented in the framework of static FDM for periodic media. Using Stokes-Helmholtz decomposition, the incompatible elastic distortion is solved from a prescribed dislocation density field with a Poisson equation. The thermodynamic-based constitutive relationships are reported for stress and double stress tensors as functions of elastic strain and elastic strain gradient tensors, respectively. Homogeneous centrosymmetric materials are considered and the case of an isotropic elastic material (Al) is considered for numerical application. Then, the compatible elastic distortion field is obtained from solving equilibrium equations through a generalized Navier-Mindlin type equation. The Fourier-based method is applied, which defines a generalized Green's function for Mindlin-type first SGE in Fourier space. Thus, the solutions for incompatible and compatible fields can be derived in the Fourier space. The efficient Fast Fourier Transform (FFT) algorithm is used based on intrinsic Discrete Fourier Transforms (DFT) as in Berbenni et al. (2014,2016). The numerical scheme is well adapted to the discrete grid to compute higher order partial derivatives with finite differences, which are transformed to the Fourier space. Therefore, using the inverse FFT, regularized dislocation density fields obtained from the present method are numerically computed for single straight dislocations like pure screw and edge dislocations using 2D FFT and centered finite-difference based differentiation rules. Elastic distortion fields as well as Cauchy stress fields are computed with the present numerical FFT-FDM based method for single screw and edge dislocations. The numerical results are discussed in comparisons with the analytical ones derived from the incompatible SGE of Mindlin type by Lazar (2021), which was based on the eigendistortion theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Stéphane Berbenni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aamgn7kgjfnpb.bib",
  "cited_by": 0,
  "doi": null,
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  "id": "aamgn7kgjfnpb",
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  "landing_url": "https://hal.univ-lorraine.fr/hal-05718314v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
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    [
      "hal",
      "1.phys.cond"
    ],
    [
      "hal",
      "1.spi.meca"
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      "hal",
      "2.phys.cond.cm-ms"
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      "hal",
      "2.spi.meca.solid"
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  "openalex": null,
  "pdf_url": "https://hal.univ-lorraine.fr/hal-05718314/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aamgn7kgjfnpb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:31Z",
      "native_id": "hal-05718314",
      "source": "hal",
      "url": "https://hal.univ-lorraine.fr/hal-05718314v2"
    }
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  "subjects": [
    {
      "field": "physics",
      "origin": "hal:1.phys.cond",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A FFT-based method for static Field Dislocation Mechanics within an isotropic first Strain Gradient Elasticity theory of Mindlin type",
  "title_text": "A FFT-based method for static Field Dislocation Mechanics within an isotropic first Strain Gradient Elasticity theory of Mindlin type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:31Z",
  "url": "https://research.draconitic.com/paper/aamgn7kgjfnpb",
  "venue": "HAL",
  "versions": []
}