Polyconvexity does not imply true-stress-true-strain monotonicity in the incompressible three-dimensional case

Dominik K. Klein; Maximilian P. Wollner; Patrizio Neff

Polyconvexity does not imply true-stress-true-strain monotonicity in the incompressible three-dimensional case

Classical Physics 2026-06-10 v1 Materials Science Mathematical Physics

Authors: Dominik K. Klein , Maximilian P. Wollner , Patrizio Neff

Abstract

We study constitutive conditions of hyperelastic potentials for incompressible material behavior in three dimensions. By means of a counterexample, we show that polyconvexity does not imply true-stress-true-strain monotonicity. Thus, polyconvexity alone is not strong enough to guarantee a physically reasonable response for idealized elasticity.

Keywords

polyconvexity true-stress-true-strain monotonicity incompressible hyperelasticity counterexample

Cite

@article{arxiv.2607.06568,
  title  = {Polyconvexity does not imply true-stress-true-strain monotonicity in the incompressible three-dimensional case},
  author = {Dominik K. Klein and Maximilian P. Wollner and Patrizio Neff},
  journal= {arXiv preprint arXiv:2607.06568},
  year   = {2026}
}

Comments

6 pages, 3 figures