{
  "abstract": "Large plastic deformation can drive an initially uniform single crystal to spontaneously subdivide into misoriented grains separated by thin dislocation walls -- a pattern-forming instability rooted in the loss of convexity of the crystal's elastic energy at large strain. We study this phenomenon for a ductile crystal in plane-strain simple shear within continuum dislocation theory, using a polyconvex (Ciarlet--Geymonat) elastic energy that guarantees existence of minimizers for the coupled deformation--slip problem. Minimizing over the plastic slip yields a condensed energy of double-well form whose non-quasiconvexity favours a lamellar microstructure; the gradient of the geometrically necessary dislocation density regularizes it, giving the grain boundaries a finite thickness and energy as functions of the misorientation angle. A block-coordinate finite element scheme -- alternating a convex non-smooth solve for the slip with a Levenberg-regularized Newton solve for the deformation -- resolves this microstructure numerically and detects its spontaneous onset, reproducing the lamellar grain structure in agreement with the closed-form analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07016",
  "author_total": 2,
  "authors": [
    {
      "name": "Khanh Chau Le"
    },
    {
      "name": "Thanh Danh Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4axaqgsvwdm1t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07016",
  "fulltext_url": null,
  "id": "4axaqgsvwdm1t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07016",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "2505|Microstructure and mechanical properties"
    ]
  ],
  "openalex": "W7212048149",
  "pdf_url": "https://arxiv.org/pdf/2609.07016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4axaqgsvwdm1t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Formation of grain boundaries in ductile single crystals under plane-strain simple shear: a block-coordinate finite element method",
  "title_text": "Formation of grain boundaries in ductile single crystals under plane-strain simple shear: a block-coordinate finite element method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/4axaqgsvwdm1t",
  "venue": "arXiv",
  "versions": []
}