Maxwell representation edit

Given that one Maxwell material has an elasticity ${\displaystyle E_{1}}$  and viscosity ${\displaystyle \eta _{1}}$ , and the other Maxwell material has an elasticity ${\displaystyle E_{2}}$  and viscosity ${\displaystyle \eta _{2}}$ , the Burgers model has the constitutive equation

${\displaystyle \sigma +\left({\frac {\eta _{1}}{E_{1}}}+{\frac {\eta _{2}}{E_{2}}}\right){\dot {\sigma }}+{\frac {\eta _{1}\eta _{2}}{E_{1}E_{2}}}{\ddot {\sigma }}=\left(\eta _{1}+\eta _{2}\right){\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}\left(E_{1}+E_{2}\right)}{E_{1}E_{2}}}{\ddot {\varepsilon }}}$ 

where ${\displaystyle \sigma }$  is the stress and ${\displaystyle \varepsilon }$  is the strain.

Kelvin representation edit

Given that the Kelvin material has an elasticity ${\displaystyle E_{1}}$  and viscosity ${\displaystyle \eta _{1}}$ , the spring has an elasticity ${\displaystyle E_{2}}$  and the dashpot has a viscosity ${\displaystyle \eta _{2}}$ , the Burgers model has the constitutive equation

${\displaystyle \sigma +\left({\frac {\eta _{1}}{E_{1}}}+{\frac {\eta _{2}}{E_{1}}}+{\frac {\eta _{2}}{E_{2}}}\right){\dot {\sigma }}+{\frac {\eta _{1}\eta _{2}}{E_{1}E_{2}}}{\ddot {\sigma }}=\eta _{2}{\dot {\varepsilon }}+{\frac {\eta _{1}\eta _{2}}{E_{1}}}{\ddot {\varepsilon }}}$ 

where ${\displaystyle \sigma }$  is the stress and ${\displaystyle \varepsilon }$  is the strain.^[1]

This model incorporates viscous flow into the standard linear solid model, giving a linearly increasing asymptote for strain under fixed loading conditions.

• Generalized Maxwell model
• Kelvin–Voigt material
• Maxwell material
• Standard linear solid model

• Creep and Stress Relaxation for Four-Element Viscoelastic Solids and Liquids, Wolfram Demonstrations Project