Skip to content
DraconiticResearch
Search Sources API
194,164 studies31 sourcesUpdated 2 min ago
PreprintarXiv licencearXiv

Vector and matrix monotonicity characterisation of the "load forces" in nonlinear elasticity: compressible versus incompressible response

  • Jendrik Voss
  • Ionel-Dumitrel Ghiba
  • Robert J. Martin
  • Patrizio Neff
Open at sourcePDFDOICite

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 Sym++(n)∩ SL(n) of positive definite symmetric tensors with unit determinant and the corresponding spectral manifold 𝒮={(λ1,dotsc,λn)∈ ℝn+ middle| λ1λ2⋯λn=1}, 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 TBiot(U), the engineering stress, or the load tensor.

Related

  1. Mini mixed finite element method for nearly incompressible linear elasticity problems
    Zhijin Guan, Yue Feng, Hehu Xie +1
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
  2. A Kernel-Aware Two-Grid Preconditioner for Cell-Centered Nearly Incompressible Elasticity
    Shubin Fu, Xiang Zhong
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  3. Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models
    Maximilian P. Wollner, Dominik K. Klein, Herbert Baaser +2
    arXivPreprintCC BY 4.0Full textMathematical physicsCondensed matterarXiv
  4. Incompressible limit for non-isentropic compressible Euler-Navier-Stokes two-phase flow model in R^3
    Chol-Ung Rim, Hakho Hong
    Electronic Journal of Differential EquationsPeer-reviewedCC BYFull textGeneral mathematicsDOAJ
  5. A Local Stabilized Isogeometric Formulation with Discontinuous Pressure for Mesh-Conforming and Immersed Analysis of Nearly Incompressible Elasticity
    Ashkan Ali Madadi, Thomas J. R. Hughes
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{voss2026vector,
  title = {{Vector and matrix monotonicity characterisation of the "load forces" in nonlinear elasticity: compressible versus incompressible response}},
  author = {Jendrik Voss and Ionel-Dumitrel Ghiba and Robert J. Martin and Patrizio Neff},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13235},
  eprint = {2610.13235},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13235},
}
RIS
TY  - UNPB
TI  - Vector and matrix monotonicity characterisation of the "load forces" in nonlinear elasticity: compressible versus incompressible response
AU  - Jendrik Voss
AU  - Ionel-Dumitrel Ghiba
AU  - Robert J. Martin
AU  - Patrizio Neff
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13235
UR  - https://arxiv.org/abs/2610.13235
AB  - 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 Sym^++(n)∩ SL(n) of positive definite symmetric tensors with unit determinant and the corresponding spectral manifold 𝒮={(λ_1,dotsc,λ_n)∈ ℝ^n_+ middle| λ_1λ_2⋯λ_n=1}, 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_Biot(U), the engineering stress, or the load tensor.
ER  -