# Boltzmann Viscoelastic Model (LAW34)

This law valid for solid elements can be used for viscoelastic materials like polymers, elastomers, glass and fluids.

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

- ${G}_{0}$
- Short time shear modulus
- ${G}_{l}$
- Long time shear modulus
- $\beta $
- Decay constant, defined as the inverse of relaxation time
${\tau}_{s}$
:
(6) $\beta =\frac{1}{{\tau}_{s}}$ ; with ${\tau}_{s}=\frac{{\eta}_{s}}{{G}_{s}}$

From Equation 4, the value of $\beta $ governs the transition from the initial modulus ${G}_{0}$ to the final modulus ${G}_{l}$ . For $t$ =0, you obtain $\Psi \left(t\right)\to {G}_{0}$ and when $t\to \infty $ , then $\Psi \left(t\right)\to {G}_{l}$ . For a linear response, put ${G}_{0}={G}_{l}$ .