{
  "abstract": "A model for predicting the residual stress gradient in a thin film segment is developed on the basis of the theory of dislocation pile-ups. The initial shear stress within the film is relaxed via the formation of a pile-up of screw dislocations against the impenetrable film-substrate interface. Plastic strain is related to the dislocation density, leading to a fundamental equation, which links the residual stress to this density. The distribution of dislocations within the pile-up for an arbitrary, non-uniform residual stress profile is derived analytically by applying the force balance condition. This results in a singular integro-differential equation for the residual stress profile. The equation is solved numerically by a collocation method for various initial stress distributions: constant, linear, parabolic, and exponential functions. The solutions demonstrate that the established residual stress profile strongly depends on the film segment's thickness-to-width ratio and the initial stress distribution. As this ratio increases, stress relaxation becomes more effective away from the film-substrate interface. In all cases, equilibrium requires a pile-up containing dislocations with both positive and negative Burgers vectors. The total number of dislocations and their density distribution vary significantly with the initial stress profile. This model provides a critical step towards more complex models of residual stress formation in constrained material systems, specifically, thin films.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12007",
  "author_total": 2,
  "authors": [
    {
      "name": "A. V. Druzhinin"
    },
    {
      "name": "C. Cancellieri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2351fgyfcdy7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12007",
  "fulltext_url": null,
  "id": "2351fgyfcdy7y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12007",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.12007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2351fgyfcdy7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2606.12007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12007"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Residual stress gradient in a thin film within the dislocation pile-up theory",
  "title_text": "Residual stress gradient in a thin film within the dislocation pile-up theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/2351fgyfcdy7y",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1063/5.0348721",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}