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Re: [Getfem-users] divergence of stress tensor


From: Huu Phuoc BUI
Subject: Re: [Getfem-users] divergence of stress tensor
Date: Fri, 19 Jan 2018 15:02:53 +0100

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?

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? 

Thank you in advance for your reply.

Best regards,
Phuoc


 



On Tue, Jan 16, 2018 at 5:32 PM, Yves Renard <address@hidden> wrote:

Dear Phuoc,

There is no specific function for that, but you have access to the Hessian ('Hess_u' for the variable u), so you have to give the _expression_ of the divergence of the stress tensor with respect to the Hessian of the variable.

Additionally, for the jumps on normal derivatives on element interfaces see http://getfem.org/userdoc/gasm_high.html#evaluating-discontinuities-across-inter-element-edges-faces

Best regards,

Yves



Le 16/01/2018 à 06:08, Huu Phuoc BUI a écrit :
Dear getfem users,

I'd like to compute the divergence of stress tensor of a linear elasticity problem which is necessary in an a posteriori error estimate.

Do you have any idea how to compute it using generic assembly of GetFEM? 

Thank you
​ in advance for your support.​


Best regards,
Phuoc


-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
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