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

## TL;DR

This paper provides a numerical overview of isotropic elastic energies in nonlinear elasticity, focusing on invertibility and monotonicity of stress-strain pairs, serving as a resource for solid mechanics research.

## Contribution

It introduces a comprehensive numerical evaluation of constitutive properties for various isotropic energies, highlighting invertibility and monotonicity in stress-strain relationships.

## Key findings

- Numerical evaluation of elastic energies for invertibility.
- Assessment of monotonicity in stress-strain pairs.
- Creation of a publicly accessible yes/no table for these properties.

## 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.