Dear Seyed,

There are two get_strain() functions 
<https://www.dealii.org/developer/doxygen/deal.II/step_18.html#Auxiliaryfunctions>
 
in step-18. The first computes the symmetric part of the shape function 
gradients, and the second computes the small strain tensor.

To store the values of the energy at each quadrature point, you can simply 
modify the PointHistory class 
<https://www.dealii.org/developer/doxygen/deal.II/step_18.html#ThecodePointHistorycodeclass>
 
to suit your needs. In its current form, a stress history variable is 
already defined and updated for each evaluation point.

Regards,
Jean-Paul

On Monday, January 16, 2017 at 11:25:43 AM UTC+1, Seyed Ali Mohseni wrote:
>
> Hi,
>
> Is it possible to compute the elastic energy for a simple 2D cube before 
> we solve the system?
> Because I checked the displacement gradients and they are 0 due to having 
> no solution probably.
>
> Hence, I wonder how would someone be able to compute the elastic energy 
> with the following formula:
>
> psi = 0.5 * lambda * tr_eps * tr_eps + mu * tr_eps_2;
>
> with 
>
> tr_eps = trace(eps);
> tr_eps_2 = trace(eps * eps);
>
> Here eps is the strain tensor and lambda as well as mu are the lamé 
> parameters, respectively.
>
> In order to compute the strain tensor eps I need the displacement 
> gradients:
>
>  eps = 0.5 * (grad_u + transpose(grad_u));
>
> And from what I checked, the get_strain() function from step-18 doesn't 
> give me the same strain tensor. It seems more like a B-operator to me.
>
> If I compute the elastic energy after I solved the system, how am I able 
> to store the energy values for each cell, so I can have access to it all 
> the time. 
>
> From Timo Heister and Thomas Wick's phase-field crack examples I learned 
> that they compute energy by means of the compute_energy() function, but it 
> seems to me like they just output the value and it is not further used 
> during computation.
>
> Kind regards,
> S. A. Mohseni 
>

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