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Table of Contents
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
HartmannNefVolumicPotential
Description
Volumetric strain density from Hartmann S.,Neff P., 2003 Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility, Int. J. Solids Struct., 40, 2767–2791. $$ \mathcal{f}(J) = \frac{1}{2}\left(J-1\right)^2 + \frac{1}{2}\left(\text{ln}J\right)^2 $$
Parameters
No parameters required