Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials: numerical evidences for invertibility and monotonicity in different stress-strain pairs

Ionel-Dumitrel Ghiba; Robert Martin; Marius Apetrii; Patrizio Neff

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arXiv · 2509.00126

Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials: numerical evidences for invertibility and monotonicity in different stress-strain pairs

Ionel-Dumitrel Ghiba·Robert Martin·Marius Apetrii·Patrizio Neff

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Abstract

As a service for the solid mechanics community we gather in this paper constitutive properties of a collective list of isotropic elastic energies for compressible materials. Of interest to us are the invertibility and monotonicity of certain stress-strain pairs. The calculations are done numerically by our own evaluation algorithm and presented in a yes/no-table. Such an overview has been missing up to now. It is intended to expand the table with further energies as time goes on and updates will be found on arxive.

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Ionel-Dumitrel Ghiba, Robert Martin, Marius Apetrii, Patrizio Neff. 2025-08-29. Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials: numerical evidences for invertibility and monotonicity in different stress-strain pairs. https://arxiv.org/abs/2509.00126

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