{
  "abstract": "Crack-tip fields govern deformation localization and failure initiation. Classical continuum fracture mechanics describes these fields through theories such as the Hutchinson-Rice-Rosengren (HRR) field for nonlinear power-law solids. However, continuum descriptions break down near cracks in soft and architected materials, where load is transmitted through discrete chains, fibers, or struts. Here, we develop a discrete crack-tip theory for lattice networks with nonlinear chains. The theory has two central components. First, at large deformation, the strain of a representative chain in layer $i$ depends approximately linearly on the applied macroscopic strain, $\\varepsilon_i\\approx k_i(λ-1)$, defining a layer-dependent strain-amplification factor $k_i$. Second, along topology-selected chain directions, termed discrete HRR lines, the layer-to-layer ratios of $k_i$ follow a two-regime scaling law. Together, for a power-law chain force-strain relation with exponent $p$, the inner discrete regime predicts $\\varepsilon_i\\sim i^{-1/p}$ and $f_i\\sim i^{-1}$, which differs from the classical continuum HRR prediction. The theory also explains why the intrinsic fracture energy approaches a size-independent limit as the network size increases. Photoelastic hydrogel experiments further validate our theory. These results reveal a two-regime crack-tip scaling law in nonlinear lattice networks and provide a framework for predicting chain deformation and intrinsic fracture energy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04568",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiabin Liu"
    },
    {
      "name": "Shaoting Lin"
    },
    {
      "name": "Juntao Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d83fcwmsvhbad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04568",
  "fulltext_url": null,
  "id": "d83fcwmsvhbad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04568",
  "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"
    ],
    [
      "openalex",
      "2210|Advanced Materials and Mechanics"
    ]
  ],
  "openalex": "W7211874944",
  "pdf_url": "https://arxiv.org/pdf/2609.04568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d83fcwmsvhbad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.04568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04568"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A discrete crack-tip theory for nonlinear lattice networks",
  "title_text": "A discrete crack-tip theory for nonlinear lattice networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/d83fcwmsvhbad",
  "venue": "arXiv",
  "versions": []
}