{
  "abstract": "A central problem in nonlinear elasto-plasticity theory is to formulate a geometrically nonlinear, large-strain model of elasto-plasticity in single crystals in which plastic flow is driven directly by the motion of dislocations and which allows for a homogenization procedure from discrete dislocation lines to dislocation densities. In this work, such a model is introduced based on two hypotheses: (1) The Small-Distortion Hypothesis posits that the total plastic distortion may be arbitrarily large but its dominant part admits a representation as a gradient, meaning that the distorting effect of dislocations is small relative to the specimen size. Concretely, this hypothesis is realized here through a \"multiplicative Helmholtz-type decomposition\", which splits an arbitrary matrix field into the product of a gradient and a matrix field with controlled curl. (2) The Line-Tension Approximation treats all dislocations as infinitesimally thin lines whose local stress fields are individually negligible compared to specimen-scale stresses and only matter in the aggregate. The resulting model, termed the Small-Distortion Geometric Model, furthermore employs the so-called Space-Time Framework, which furnishes a geometric language to precisely describe the advection of dislocation lines. As such, it provides a physically grounded account of crystal plasticity in an idealized mesoscopic setting that bridges dislocation mechanics and continuum elasto-plasticity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23728",
  "author_total": 1,
  "authors": [
    {
      "name": "Filip Rindler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/98epwdzqfgwhp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23728",
  "fulltext_url": null,
  "id": "98epwdzqfgwhp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23728",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "2505|Microstructure and mechanical properties"
    ]
  ],
  "openalex": "W7214049947",
  "pdf_url": "https://arxiv.org/pdf/2609.23728",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/98epwdzqfgwhp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23728",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23728"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A small-distortion geometric model for elasto-plasticity in single crystals driven by the motion of dislocations",
  "title_text": "A small-distortion geometric model for elasto-plasticity in single crystals driven by the motion of dislocations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/98epwdzqfgwhp",
  "venue": "arXiv",
  "versions": []
}