Can I perform a stress boundary condition via velocity gradient?
 

Hi,
I'm using a geodynamics program called Underworld2 to simulate earth's mantle convection.
Underworld only provide boundary conditions for velocity, but I want to perform a stress boundary condition like:
in a 2D box,
sigma_12 = sigma_22 = 0 at x2 = 0

Can I perform this via velocity Neumann boundary condition?

Thanks for viewing this post.

I think you can, as long as the shear stress is proportional to the velocity gradient. That is also generally how we apply zero-stress conditions.

Thank you for your reply.
How? I think sigma_22 = 0 can be performed by setting (partial u2/partial x2) = 0. But as to sigma_12 = 0, there's no way to set (partial u2/partial x1 + partial u1/partial x2) = 0.

I am not sure about your geometry, but at the boundary, you usually have one gradient vanish, maybe, for example, partial u2/partial x1 =0, so you can calculate the other. due to no penetration condition.

I am not sure about your geometry, but at the boundary, you usually have one gradient vanish, maybe, for example, partial u2/partial x1 =0, so you can calculate the other. due to no penetration condition.

In a fluid, the newtonian constitutive law expresses the relation between the deviatoric stress and the velocity gradient as 2*mu*Grad v. You can have zero stress if the model assume mu=0, independently from the velocity gradient. Conversely, you have to seto to zero all the entries of tensor and consider also the natural boundary conditions on the velocity