Type of viscoelastic 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 .
Maxwell representation [ edit ] Schematic diagram of Burgers material, Maxwell representation Given that one Maxwell material has an elasticity E 1 {\displaystyle E_{1}} and viscosity η 1 {\displaystyle \eta _{1}} , and the other Maxwell material has an elasticity E 2 {\displaystyle E_{2}} and viscosity η 2 {\displaystyle \eta _{2}} , the Burgers model has the constitutive equation
σ + ( η 1 E 1 + η 2 E 2 ) σ ˙ + η 1 η 2 E 1 E 2 σ ¨ = ( η 1 + η 2 ) ε ˙ + η 1 η 2 ( E 1 + E 2 ) E 1 E 2 ε ¨ {\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 σ {\displaystyle \sigma } is the stress and ε {\displaystyle \varepsilon } is the strain.
Kelvin representation [ edit ] Schematic diagram of Burgers material, Kelvin representation Given that the Kelvin material has an elasticity E 1 {\displaystyle E_{1}} and viscosity η 1 {\displaystyle \eta _{1}} , the spring has an elasticity E 2 {\displaystyle E_{2}} and the dashpot has a viscosity η 2 {\displaystyle \eta _{2}} , the Burgers model has the constitutive equation
σ + ( η 1 E 1 + η 2 E 1 + η 2 E 2 ) σ ˙ + η 1 η 2 E 1 E 2 σ ¨ = η 2 ε ˙ + η 1 η 2 E 1 ε ¨ {\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 σ {\displaystyle \sigma } is the stress and ε {\displaystyle \varepsilon } is the strain.[ 1]
Model characteristics [ edit ] Comparison of creep and stress relaxation for three and four element models This model incorporates viscous flow into the standard linear solid model , giving a linearly increasing asymptote for strain under fixed loading conditions.
^ Malkin, Alexander Ya.; Isayev, Avraam I. (2006). Rheology: Concepts, Methods, and Applications . ChemTec Publishing. pp. 59–60. ISBN 9781895198331 .