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Stress Tensor

The Stress tensor is the sum of the Hydrostatic Stress tensor, $ -p\delta_{ij}$, and of the Viscous Stress tensor, $ P_{ij}$:

$\displaystyle T_{ij} = -p\delta_{ij} + P_{ij}$

Direct stresses: $ T_{11}$, $ T_{22}$, $ T_{33}$
Shear stresses: $ T_{12}$, $ T_{13}$, $ T_{21}$, $ T_{23}$, $ T_{31}$, $ T_{32}$
The Stokesian Stress tensor (Stokesian fluid):

$\displaystyle T_{ij} = (-p + \alpha)\delta_{ij} + \beta e_{ij} + \gamma e_{ik}e_{kj}$

The Newtonian Stress tensor (Newtonian fluid):

$\displaystyle T_{ij} = (-p + \lambda\Theta)\delta_{ij} + 2\mu e_{ij}$



Alexis Angelidis (PhD) 2004-02-09