{
  "abstract": "A common approach to studying elastic localization is to pose the problem on an infinite domain, avoiding explicit treatment of the end conditions. For a finite structure, this approach raises a natural question: how long must the structure be for the infinite-domain approximation to become accurate, and how large is the resulting error? To address this question, we develop a constructive method that provides an explicit length threshold beyond which the approximation error is small and explicitly bounded. Applied to a prototypical model arising from localized buckling of a twisted rod, the method yields the threshold and error bounds analytically. The threshold is found to vary with loading, showing that whether the infinite-domain approximation is appropriate depends on both structural length and loading state. The load-dependent length threshold also clarifies the validity of weakly nonlinear analysis: the finite-domain expansion is appropriate only over a limited range near bifurcation, beyond which the infinite-domain expansion is more appropriate. The method is then applied to the fully nonlinear problem of localized bulging in cylindrical membrane tubes. Numerical evaluation of the model-dependent estimates yields a length threshold and an upper bound on the approximation error, while direct comparisons of the finite- and infinite-domain solutions support these predictions. Together, these results characterize the applicability of the infinite-domain approximation and weakly nonlinear description to elastic localization in finite structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15312",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiang Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0beyexxbj3fgs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15312",
  "fulltext_url": null,
  "id": "0beyexxbj3fgs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15312",
  "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.soft"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "openalex",
      "2211|Elasticity and Wave Propagation"
    ]
  ],
  "openalex": "W7164923438",
  "pdf_url": "https://arxiv.org/pdf/2606.15312",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0beyexxbj3fgs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2606.15312",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15312"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Elastic localization in finite structures: assessment of the infinite-domain approximation and validity of weakly nonlinear analysis",
  "title_text": "Elastic localization in finite structures: assessment of the infinite-domain approximation and validity of weakly nonlinear analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/0beyexxbj3fgs",
  "venue": "arXiv",
  "versions": []
}