{
  "abstract": "We construct a compressible isotropic energy on $\\mathrm{GL}^+(3)$ combining polyconvexity and global true-stress-true-strain monotonicity (TSTS-M++), answering a question of Wollner, Holzapfel and Neff. For every $μ>0$ and $k>0$, the energy $W_k(F)=\\fracμ{2k}[\\exp(k(\\lVert F\\rVert^2+3J^{-1}+J-7))-1]$, $J=\\det F$, is polyconvex and strictly rank-one convex. Its Cauchy-stress response satisfies TSTS-M++ globally if and only if $k\\ge1/(8\\sqrt3)$. The reference state is stress free with positive infinitesimal shear and bulk moduli. Stress bijectivity has the smaller sharp threshold $k_{\\rm B}\\approx0.0083$: at equality the stress map is a global homeomorphism with a nondifferentiable inverse, and above it a global smooth diffeomorphism. Thus, for $k_{\\rm B}\\le k<1/(8\\sqrt3)$, the Cauchy-stress map remains globally bijective while TSTS-M++ fails at finite strain. In the TSTS-M++ regime, each prescribed inner radius of a finite plane-strain annulus with a traction-free outer wall has a unique radial equilibrium, and the inner pressure increases smoothly and strictly from zero to infinity. Comparisons with other energies distinguish the roles of polyconvexity, TSTS-M++, reduced convexity and endpoint growth. Under incompressible spherical inflation, global pressure inversion holds for the Demiray family with $b\\ge b_*$, including $W_k|_{J=1}$ for $k\\ge k_*$ and the stress-free $I_1$-exponential energy, and for the exponentiated Hencky energy when $k_{\\mathrm{eH}}>3/8$. Incompressible neo-Hooke instead has a limit point. A further compressible $I_1$ energy retains the global constitutive properties and reference moduli of $W_k$ but exhibits two pressure turning points under incompressible spherical inflation, showing that these properties allow a descending pressure branch.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06026",
  "author_total": 5,
  "authors": [
    {
      "name": "Dongxin Bai"
    },
    {
      "name": "Yunhao Wu"
    },
    {
      "name": "Yong Li"
    },
    {
      "name": "Kai Zhang"
    },
    {
      "name": "Patrizio Neff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78ga3bn5t9vgg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06026",
  "fulltext_url": null,
  "id": "78ga3bn5t9vgg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06026",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2204|Elasticity and Material Modeling"
    ]
  ],
  "openalex": "W7212074998",
  "pdf_url": "https://arxiv.org/pdf/2609.06026",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78ga3bn5t9vgg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2609.06026",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06026"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A globally defined compressible polyconvex isotropic energy satisfying the true-stress-true-strain monotonicity condition (TSTS-M++)",
  "title_text": "A globally defined compressible polyconvex isotropic energy satisfying the true-stress-true-strain monotonicity condition (TSTS-M++)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/78ga3bn5t9vgg",
  "venue": "arXiv",
  "versions": []
}