- #1

da_willem

- 599

- 1

[tex]2 \mu (e_{ij} -\frac{1}{3} \Delta \delta _{ij} )^2 = 2 \mu ( e_{ij}^2 - \frac{1}{3} \Delta ^2 )= \frac{d_{ij}}{2 \mu}[/tex]

with [itex]\mu[/itex] the dynamic viscosity, e the rate-of-deformation tensor, [itex]\Delta[/tex] the divergence of the velocity and d the deviatoric stresses. I assume these squares express two sums required by the Einstein summation convention?

I also found some expressions for the deviatoric stresses in cylindrical coordinates, terms like [tex]d_{z \phi}, d_{zr}, d_{zz}[/tex] etc. I don't really know how to interpret these and how to proceed. Can I use the last expression and instead of summing over x,y and z sum over the three cylindrical coordinates? Or does this yield something different?