====== Volumic Potentials ======
The ''VolumicPotential'' material law regroups all the functions $\mathcal{f}(J)$ such that the volumetric part of the strain-energy density function $W_{vol}$ can be expressed as
$$
W_{vol} = k_0\mathcal{f}(J)
$$
with the compression modulus $k_0$ defined on the material level.

===== QuadraticVolumicPotential =====

=== Description ===
Quadratic volumetric strain density (default for ''FunctionBasedHyperMaterial'')
$$
\mathcal{f}(J) = \frac{1}{2}\left(J-1\right)^2
$$

=== Parameters ===
No parameters required


===== LogarithmicVolumicPotential =====

=== Description ===
Logarithmic volumetric strain density
$$
\mathcal{f}(J) = \frac{1}{2}\left(\text{ln}J\right)^2
$$

=== Parameters ===
No parameters required

===== QuadLogVolumicPotential =====

=== Description ===
Quadratic-Logarithmic volumetric strain density (same as ''NeoHookeanHyperMaterial'' and ''MooneyRivlinHyperMaterial'')
$$
\mathcal{f}(J) = \frac{1}{2}\left(J-1\right)^2 + \frac{1}{2}\left(\text{ln}J\right)^2
$$

=== Parameters ===
No parameters required

===== HartmannNeffVolumicPotential =====

=== Description ===
Volumetric strain density from {{:doc:user:references:materials:2003_polyconvexity_of_generalized_polynomial_type_hyperelastic_strain_energy_function_Hartmann_Neff.pdf|Hartmann S.,Neff P., 2003 Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility, Int. J. Solids Struct., 40, 2767–2791.}}
$$
\mathcal{f}(J) = \frac{1}{50}\left(J^5+J^{-5}-2\right)
$$

=== Parameters ===
No parameters required


===== MieheVolumicPotential =====

=== Description ===
Volumetric strain density from {{https://onlinelibrary.wiley.com/doi/10.1002/nme.1620371202|Miehe C., 1994, Aspects of the formulation and finite element implementation of large strain isotropic elasticity, Int. J. Numer. Meth. Engng., 37, 1981–2004.}}
$$
\mathcal{f}(J) = J - \text{ln}J -1
$$

=== Parameters ===
No parameters required


===== SimoTaylorVolumicPotential =====

=== Description ===
Volumetric strain density from {{:doc:user:references:materials:1991_quasi-incompressible_finite_elasticity_in_principal_stretches_continuum_basis_and_numerical_algorithms_simo_taylor.pdf|Simo J., Taylor R., 1991, Quasi-incompressible finite elasticity in principal stretches. continuum basis and numerical algorithms, Comput. Methods Appl. Mech. Eng., 85, 273–310.}}
$$
\mathcal{f}(J) = \frac{1}{4}\left( J^2 - 2\text{ln}J - 1 \right)
$$

=== Parameters ===
No parameters required



===== OgdenVolumicPotential =====

=== Description ===
Volumetric strain density from {{:doc:user:references:materials:1972_large_deformation_isotropic_elasticity_on_the_correlation_of_theory_and_experiment_for_incompressible_rubberlike_solids_Ogden.pdf|Ogden R. W., 1972, Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond., 326, 565–584.}}
$$
\mathcal{f}(J) = \frac{1}{\beta^2}\left( \beta\text{ln}J + J^{-\beta} - 1 \right)
$$
where $\beta$ is an experimentally determined material parameter.

=== Parameters ===
^   Name                                                  ^  Metafor Code  ^ Dependency ^
| Ogden beta parameter ($\beta$)  |  ''HYPER_OGDEN_BETA''  |  ''TO/TM''  |