{
  "abstract": "In this paper, we study the relation between different notions of monotonicity for isotropic hyperelastic compressible and incompressible materials. We study how to define the monotonicity concept on the manifold $\\rm{Sym}^{++}(n)\\cap \\rm{SL}(n)$ of positive definite symmetric tensors with unit determinant and the corresponding spectral manifold $\\mathcal S=\\left\\{(λ_1,\\dotsc,λ_n)\\in \\mathbb{R}^n_+\\,\\middle|\\, λ_1λ_2\\cdotsλ_n=1\\right\\}$, and give a precise characterisation of monotonicity in the case of hyperelastic materials. In particular, we consider the monotonicity properties of the Biot stress tensor $T_{\\rm Biot}(U)$, the engineering stress, or the load tensor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13235",
  "author_total": 4,
  "authors": [
    {
      "name": "Jendrik Voss"
    },
    {
      "name": "Ionel-Dumitrel Ghiba"
    },
    {
      "name": "Robert J. Martin"
    },
    {
      "name": "Patrizio Neff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/an91ab6yfne7a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13235",
  "fulltext_url": null,
  "id": "an91ab6yfne7a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13235",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2204|Elasticity and Material Modeling"
    ]
  ],
  "openalex": "W7221565991",
  "pdf_url": "https://arxiv.org/pdf/2610.13235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/an91ab6yfne7a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Vector and matrix monotonicity characterisation of the \"load forces\" in nonlinear elasticity: compressible versus incompressible response",
  "title_text": "Vector and matrix monotonicity characterisation of the \"load forces\" in nonlinear elasticity: compressible versus incompressible response",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/an91ab6yfne7a",
  "venue": "arXiv",
  "versions": []
}