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arXiv · 2610.13235

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
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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.

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Jendrik Voss, Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff. 2026-10-09. Vector and matrix monotonicity characterisation of the "load forces" in nonlinear elasticity: compressible versus incompressible response. https://arxiv.org/abs/2610.13235

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