{
  "abstract": "Quasi-brittle fracture is prevalent in concrete, rock, ceramics, composites, and masonry, and its simulation faces a trade-off among accuracy, efficiency, and simplicity. The classical Lattice Spring Model (LSM) captures cracking via bond breakage without remeshing, but its elements are empirical and limited to a few tessellable shapes with fixed Poisson's ratios. We propose a tessellated Isotropic Elastic Lattice Spring Model (IELSM) that discretizes continua into polygonal elements with axial springs and a volumetric constraint, achieving isotropic elasticity on arbitrary polygonal tessellations. Macroscopic isotropy reduces to governing equations whose solvability gives a theoretical criterion for element admissibility, proving conventional tessellable elements and extending to arbitrary regular N-gons and concave elements. Exploiting boundary interpolation compatibility with finite elements, IELSM is assembled by direct node sharing, without interface elements or kinematic constraints. Coupled with an isotropic damage model, a pure bending test and four fracture benchmarks show that the coupling preserves displacement accuracy, yields crack paths and load-displacement curves agreeing with experiments and outperforming standard FEM, and is insensitive to mesh refinement. IELSM can also be restricted to damage-prone regions, with the remainder modeled by finite elements via node sharing. For the benchmarks, this reduces nodes by 41.2-80.9% and CPU time by 34.2-85.2% versus full-domain IELSM. The framework advances IELSM element construction from empirical trial and error to theoretical determination and simplifies coupling to node sharing, offering a balanced route for complex quasi-brittle fracture analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28970",
  "author_total": 2,
  "authors": [
    {
      "name": "D. M. LI"
    },
    {
      "name": "Meng-Cheng HE"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3rmrnhj5pazpm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28970",
  "fulltext_url": null,
  "id": "3rmrnhj5pazpm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28970",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.28970",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3rmrnhj5pazpm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28970",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28970"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Tessellated Isotropic Elastic Lattice Spring Model for Quasi-Brittle Fracture",
  "title_text": "Tessellated Isotropic Elastic Lattice Spring Model for Quasi-Brittle Fracture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/3rmrnhj5pazpm",
  "venue": "arXiv",
  "versions": []
}