Burgers material

A Burgers material is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the Dutch physicist Johannes Martinus Burgers.

Overview

= Maxwell representation =

File:Burgers model 2.svg

Given that one Maxwell material has an elasticity $E_1$ and viscosity $\eta_1$ , and the other Maxwell material has an elasticity $E_2$ and viscosity $\eta_2$ , the Burgers model has the constitutive equation

: $\sigma + \left( \frac {\eta_1} {E_1} + \frac {\eta_2} {E_2} \right) \dot\sigma +
\frac {\eta_1 \eta_2} {E_1 E_2} \ddot\sigma = \left( \eta_1 + \eta_2 \right) \dot\varepsilon +
\frac {\eta_1 \eta_2 \left( E_1 + E_2 \right)} {E_1 E_2} \ddot\varepsilon$

where $\sigma$ is the stress and $\varepsilon$ is the strain.

= Kelvin representation =

File:Burgers model.svg

Given that the Kelvin material has an elasticity $E_1$ and viscosity $\eta_1$ , the spring has an elasticity $E_2$ and the dashpot has a viscosity $\eta_2$ , the Burgers model has the constitutive equation

: $\sigma + \left( \frac {\eta_1} {E_1} + \frac {\eta_2} {E_1} + \frac {\eta_2} {E_2} \right) \dot\sigma +
\frac {\eta_1 \eta_2} {E_1 E_2} \ddot\sigma = \eta_2\dot\varepsilon +
\frac {\eta_1 \eta_2} {E_1} \ddot\varepsilon$

where $\sigma$ is the stress and $\varepsilon$ is the strain.{{cite book|last1=Malkin|first1=Alexander Ya.|last2=Isayev|first2=Avraam I.|title=Rheology: Concepts, Methods, and Applications|year=2006|publisher=ChemTec Publishing|isbn=9781895198331|pages=59–60}}

Model characteristics

File:Comparison three four element models.svg

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

References

External links

[http://demonstrations.wolfram.com/CreepAndStressRelaxationForFourElementViscoelasticSolidsAndL/ Creep and Stress Relaxation for Four-Element Viscoelastic Solids and Liquids], Wolfram Demonstrations Project

Category:Non-Newtonian fluids