Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13235

Authors: Voss, Jendrik, Ghiba, Ionel-Dumitrel, Martin, Robert J., Neff, Patrizio

Institutions: TU Dortmund University, Alexandru Ioan Cuza University, Academia Română, Filiala Iași, Romanian Academy, University of Duisburg-Essen

Language: English

Topic: Elasticity and Material Modeling

Subfield: Biomedical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii

OpenAlex ID: W7221565991

Cites: 9

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Related to: 10