# Generalized Kelvin-Voigt Model (LAW35)

This law uses a generalized viscoelastic Kelvin-Voigt model whereas the viscosity is based on the Navier equations.

The effect of the enclosed air is taken into account via a separate pressure versus compression function. For open cell foam, this function may be replaced by an equivalent "removed air pressure" function. The model takes into account the relaxation (zero strain rate), creep (zero stress rate), and unloading. It may be used for open cell foams, polymers, elastomers, seat cushions, dummy paddings, etc. In Radioss the law is compatible with shell and solid meshes.

for $i\ne j$

for $i=j$

$\lambda $
and
${\eta}_{0}$
are the Navier Stokes viscosity coefficients which can be
compared to Lame constants in elasticity.
$\lambda +\frac{2{\eta}_{0}}{3}$
is called the volumetric coefficient of viscosity. For
incompressible model,
${\epsilon}_{kk}^{v}=0$
and
$\lambda \to \infty $
and
${\mu}_{0}=\frac{\mu}{3}$
. In Equation 11, `C`_{1}, `C`_{2} and
`C`_{3}
are Boolean multipliers used to define different responses. For example, `C`_{1}=1,
`C`_{2}=`C`_{3}=0 refers to a linear bulk model. Similarly, `C`_{1}=`C`_{2}=`C`_{3}=1
corresponds to a visco-elastic bulk model.

- $\gamma $
- Volumetric strain
- $\text{\Phi}$
- Porosity
- ${P}_{0}$
- Initial air pressure

In Radioss, the pressure may also be computed with the $P$ versus $\mu =\frac{\rho}{{\rho}_{0}}-1$ , by a user-defined function. Air pressure may be assumed as an "equivalent air pressure" versus $\mu $ . You can define this function used for open cell foams or for closed cell by defining a model identical to material LAW 33 (FOAM_PLAS).