Английская Википедия:Burgers material

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Шаблон:Short description 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

Файл:Burgers model 2.svg

Schematic diagram of Burgers material, Maxwell representation

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

<math> \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</math> where <math>\sigma</math> is the stress and <math>\varepsilon</math> is the strain.

Kelvin representation

Файл:Burgers model.svg

Schematic diagram of Burgers material, Kelvin representation

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

<math> \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</math> where <math>\sigma</math> is the stress and <math>\varepsilon</math> is the strain.

Model characteristics

Файл:Comparison three four element models.svg

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.

See also

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

External links

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