Re: [Getfem-users] divergence of stress tensor

[Konstantinos Poulios]

Dear Phuoc,

see my answers below:

On Fri, Jan 19, 2018 at 3:02 PM, Huu Phuoc BUI <address@hidden> wrote:

Dear Yves,

Thank you for your reply!

We expressed the divergence of stress tensor with respect to the variable u. In the _expression_, we have something like Grad(Trace(Grad_u)), and Trace(Hess_u). When assembling these terms with GetFEM, there is an error in assembly string. I tried to assembly separately these two terms. Both did not work.

For the first term Grad(Trace(Grad_u)), I think the error comes from the fact that, in GetFEM, we can only use Grad operator with a variable, i.e., Grad_u, Grad_Test_u, etc. Therefore, we can not write directly Grad(Trace(Grad_u)). Is it right?

Correct.

 

For the second term Trace(Hess_u), I think the error comes from the Trace operator, since in the GetFEM documentation, it is stated that Trace operator is used for a square matrix. In our case, since u is a vector field, Hess_u is a tensor of order 3. Can we use Trace operator in assembly string for a tensor of order 3?

What should the trace of a 3rd order tensor be? Lets say H_ijk is a 3 order tensor. If e.g. you want to calculate a vector

v_i = H_ikk (summation over k), as far as I remember you can get it with "H:Id(3)", please try.

 

Thank you in advance for your reply.

Best regards,

Phuoc

Best regards

Kostas