{
  "abstract": "We present a fully variational, model-independent formulation of the Cut Finite Element Method (CutFEM) for finite-strain elasticity. The discrete problem is derived from a single augmented energy functional consisting of the bulk hyperelastic energy, the Nitsche terms that impose the boundary conditions weakly, and the ghost-penalty stabilisation. At each nonlinear iterate, the residual is the exact first variation of this functional with the adaptive Nitsche weight frozen, while the correction uses a symmetric, coercive approximation of its Hessian. Automatic differentiation (AD) generates the first Piola--Kirchhoff stress tensor and the elasticity tensor directly from the scalar energy density, avoiding manual re-derivation when exchanging hyperelastic models. To our knowledge, this is the first unfitted finite-strain scheme combining an energy-only, model-independent construction with AD and an accuracy analysis at unfitted boundaries. Analysis of the linearised problem solved at each quasi-Newton step establishes cut-independent coercivity, continuity, and an $O(h^{-2})$ condition number bound, yielding a quasi-optimal convergence theorem for regular solutions through the Brezzi--Rappaz--Raviart framework. Numerically, the method attains optimal $h$-convergence for quadratic and cubic elements on a smooth test case. Furthermore, we quantify the method's accuracy limit at mixed Dirichlet--Neumann junctions using the Kolosov--Muskhelishvili characteristic equation. The exact solution's corner singularity caps the convergence rate identically for fitted and unfitted methods. Local mesh refinement removes this bound: we verify the recovery of optimal rates numerically for first-order elements, and prove that the unfitted discretisation inherits the rate the underlying refinement attains, with cut-independent constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.02334",
  "author_total": 2,
  "authors": [
    {
      "name": "Michał Tomasz Wichrowski"
    },
    {
      "name": "Ella Godiva Noomen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/112vwdb66jmtx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.02334",
  "fulltext_url": null,
  "id": "112vwdb66jmtx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.02334",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.02334",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/112vwdb66jmtx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2607.02334",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.02334"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Unified CutFEM Formulation for Finite-Strain Elasticity: Energy Minimisation and Corner Singularities",
  "title_text": "A Unified CutFEM Formulation for Finite-Strain Elasticity: Energy Minimisation and Corner Singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/112vwdb66jmtx",
  "venue": "arXiv",
  "versions": []
}