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

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.