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doc:user:elements:volumes:hyper_vol_potential

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doc:user:elements:volumes:hyper_vol_potential [2025/11/14 11:06] – [HartmannNefVolumicPotential] vanhulledoc:user:elements:volumes:hyper_vol_potential [2026/07/02 14:25] (current) – vanhulle
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 ====== Volumic Potentials ====== ====== 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+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) W_{vol} = k_0\mathcal{f}(J)
 $$ $$
-with the compression modulus $k_0$ defined on the material level.+with the compression modulus $k_0$.
  
 ===== QuadraticVolumicPotential ===== ===== QuadraticVolumicPotential =====
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 === Parameters === === Parameters ===
-No parameters required+^   Name                                                  ^  Metafor Code  ^ Dependency ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  |
  
  
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 === Parameters === === Parameters ===
-No parameters required+^   Name                                                  ^  Metafor Code  ^ Dependency ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  | 
  
 ===== QuadLogVolumicPotential ===== ===== QuadLogVolumicPotential =====
Line 38: Line 41:
  
 === Parameters === === Parameters ===
-No parameters required+^   Name                                                  ^  Metafor Code  ^ Dependency ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  |
  
-===== HartmannNefVolumicPotential =====+===== HartmannNeffVolumicPotential =====
  
 === Description === === 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.}} 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}{2}\left(J-1\right)^2 + \frac{1}{2}\left(\text{ln}J\right)^2+\mathcal{f}(J) = \frac{1}{50}\left(J^5+J^{-5}-2\right)
 $$ $$
  
 === Parameters === === Parameters ===
-No parameters required+^   Name                                                  ^  Metafor Code  ^ Dependency ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  | 
 + 
 + 
 +===== 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 === 
 +^   Name                                                  ^  Metafor Code  ^ Dependency ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  | 
 + 
 + 
 +===== 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 === 
 +^   Name                                                  ^  Metafor Code  ^ Dependency ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  | 
 + 
 + 
 +===== 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 ^ 
 +| Compression modulus ($k_0$)  |  ''HYPER_COMPR_MODULUS''  |  ''TO/TM''  | 
 +| Ogden beta parameter ($\beta$)  |  ''HYPER_OGDEN_BETA''  |  ''TO/TM''  | 
doc/user/elements/volumes/hyper_vol_potential.1763114778.txt.gz · Last modified: by vanhulle
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