{
  "abstract": "In order to obtain the displacement field, both generally in the case of an arbitrary body force and specifically in the case of a conservative body force, the mechanical problem of statics of three-dimensional stress-gradient non-local medium is analytically solved on unbounded domain by considering a system of equations consisting of an equilibrium equation, infinitesimal strain, and both scalar- and tensor-type stress-gradient Eringen three-dimensional models. Since the system of equations is linear, for each model the solution is obtained in the form of a superposition of the local-type displacement field, common to each model, and the non-local-type displacement field, specific to the non-locality operator of the model. Among the three scalar-type and five tensor-type considered models, six distinct analytical displacement field expressions are obtained for an arbitrary body force: one expression specific to a scalar-type model, three specific to individual tensor-type models, while each of the remaining two expressions are common to one scalar- and one tensor-type model. The displacement vector fields are graphically represented in the case of gravitational body force, yielding five different models, since two tensor-type models become the same when the force is conservative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39888",
  "author_total": 2,
  "authors": [
    {
      "name": "Slađan Jelić"
    },
    {
      "name": "Dušan Zorica"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bdyq9rcjjcpy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39888",
  "fulltext_url": null,
  "id": "9bdyq9rcjjcpy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39888",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bdyq9rcjjcpy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Three-dimensional stress-gradient non-locality problem: Displacement field for an arbitrary and a conservative force",
  "title_text": "Three-dimensional stress-gradient non-locality problem: Displacement field for an arbitrary and a conservative force",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9bdyq9rcjjcpy",
  "venue": "arXiv",
  "versions": []
}