viscosité extensionnelle

{\displaystyle z </span referrerpolicy=

{\displaystyle \eta _{e}={\frac {\sigma _{zz}-{\frac {1}{2}}\sigma _{xx}-{\frac {1}{2}}\sigma _{yy}}{\dot {\varepsilon }}}\,\! <semantics><mrow><mstyle><msub><mi>η</mi><mrow><mi>e</mi></mrow></msub><mo>=</mo><mrow><mfrac><mrow><msub><mi>σ</mi><mrow><mi>z</mi><mi>z</mi></mrow></msub><mo>−</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><msub><mi>σ</mi><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>−</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><msub><mi>σ</mi><mrow><mi>y</mi><mi>y</mi></mrow></msub></mrow><mrow><mover><mi>ε</mi><mo>˙</mo></mover></mrow></mfrac></mrow><mspace></mspace><mspace></mspace></mstyle></mrow><annotation>{\displaystyle \eta _{e}={\frac {\sigma _{zz}-{\frac {1}{2}}\sigma _{xx}-{\frac {1}{2}}\sigma _{yy}}{\dot {\varepsilon }}}\,\!}</annotation></semantics></math></span><img src=

où

{\displaystyle \eta _{e}\,\! <semantics><mrow><mstyle><msub><mi>η</mi><mrow><mi>e</mi></mrow></msub><mspace></mspace><mspace></mspace></mstyle></mrow><annotation>{\displaystyle \eta _{e}\,\!}</annotation></semantics></math></span><img src=

viscosité extensionnelle ou viscosité d'élongation

{\displaystyle \sigma _{nn}\,\! <semantics><mrow><mstyle><msub><mi>σ</mi><mrow><mi>n</mi><mi>n</mi></mrow></msub><mspace></mspace><mspace></mspace></mstyle></mrow><annotation>{\displaystyle \sigma _{nn}\,\!}</annotation></semantics></math></span><img src=

contrainte normale le long de la direction n.

{\displaystyle {\dot {\varepsilon }}\,\! <semantics><mrow><mstyle><mrow><mrow><mover><mi>ε</mi><mo>˙</mo></mover></mrow></mrow><mspace></mspace><mspace></mspace></mstyle></mrow><annotation>{\displaystyle {\dot {\varepsilon }}\,\!}</annotation></semantics></math></span><img src=

taux de déformation :

{\displaystyle {\dot {\varepsilon }}={\frac {\partial v_{z}}{\partial z}}\,\! <semantics><mrow><mstyle><mrow><mrow><mover><mi>ε</mi><mo>˙</mo></mover></mrow></mrow><mo>=</mo><mrow><mfrac><mrow><mi>∂</mi><msub><mi>v</mi><mrow><mi>z</mi></mrow></msub></mrow><mrow><mi>∂</mi><mi>z</mi></mrow></mfrac></mrow><mspace></mspace><mspace></mspace></mstyle></mrow><annotation>{\displaystyle {\dot {\varepsilon }}={\frac {\partial v_{z}}{\partial z}}\,\!}</annotation></semantics></math></span><img src=

Le rapport entre la viscosité extensionnelle ${\displaystyle \eta _{e <semantics><mrow><mstyle><msub><mi>η</mi><mrow><mi>e</mi></mrow></msub></mstyle></mrow><annotation>{\displaystyle \eta _{e}}</annotation></semantics></math></span><img src=$ ${\displaystyle \eta <semantics><mrow><mstyle><mi>η</mi></mstyle></mrow><annotation>{\displaystyle \eta }</annotation></semantics></math></span><img src=$ ${\displaystyle \mathrm {Tr} =\eta _{e}/\eta <semantics><mrow><mstyle><mrow><mi>T</mi><mi>r</mi></mrow><mo>=</mo><msub><mi>η</mi><mrow><mi>e</mi></mrow></msub><mrow><mo>/</mo></mrow><mi>η</mi></mstyle></mrow><annotation>{\displaystyle \mathrm {Tr} =\eta _{e}/\eta }</annotation></semantics></math></span><img src=$