{
  "abstract": "In a previous work [Masubuchi et al., Compos. Sci. Technol. 134, 43 (2016)], a fiber-length distribution function was proposed as the hypoexponential, or Erlang-type, convolution of two exponential waiting lengths, motivated by two independent Poisson processes for breakage and for blocking of adjacent breaks. The present paper further evaluates this hypoexponential form by introducing a finite initial length L_{0}, and by analyzing the mechanistic basis of the buckling-induced fiber breakage process. The obtained finite-L_{0} closed-form solution was compared to a glass fiber dataset to retroactively justify the infinite-length idealization in the earlier work for such systems while providing the complete form for processes in which fragments remain comparable to L_{0}. Concerning the mechanics of fiber fragmentation, a Mellin transform analysis of the fragmentation equation showed that scale-invariant cascades yield power laws and therefore cannot generate characteristic lengths; those lengths must instead arise from scale-breaking ingredients, particularly the cutoff region and the arrested processing history. Monte Carlo simulations of a phenomenological finite-opportunity cascade showed that the hypoexponential form does not reproduce the peak of the generated distribution but captures its exponential-like tail, implying that it serves as a useful two-parameter fitting model, although not an exact generative distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20312",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuichi Masubuchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c6fbhg29ne25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20312",
  "fulltext_url": null,
  "id": "6c6fbhg29ne25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20312",
  "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.soft"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20312",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c6fbhg29ne25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20312",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20312"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "The hypoexponential form for the fiber-length distribution in thermoplastic composites revisited: finite initial length, cascade fracture, and its mechanistic status",
  "title_text": "The hypoexponential form for the fiber-length distribution in thermoplastic composites revisited: finite initial length, cascade fracture, and its mechanistic status",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/6c6fbhg29ne25",
  "venue": "arXiv",
  "versions": []
}