On 11/15/2013 10:13 AM, Anastasia Konovalova wrote:

Thanks for the answer, Robert! And excuse me for the long response.

I'm not sure, that I understand you clearly. I have added changes from Git, and the computation of determinant in my programm is correct now. And your "black magic" code don't produce error any more. So you repaired this old bag, right?) And strain can be used for further computations now? Thank you very much!

Yes, it should work ok now.

As for the terms and issues, I compute determinant and other values for the energy calculation. If it is possible to make terms for the energy density function for hyperelastic material, it would be great and I'll add the issue as soon as I can:)

Yes, that would be possible. Add the issue, please, so that it is not forgotten.

Cheers, r.

четверг, 7 ноября 2013 г., 16:34:59 UTC+6 пользователь Robert Cimrman написал:

...

Hi Anastasia,

great job, you have just found a very old bug!

The following code (to be added in stress_strain() after i3 computation) should not raise errors but it does:

  # black magic here...
  cache =

state.variables['u'].evaluate_cache['tl_common'][0][('__v_o1', 0, 0, 'volume', None)]

  from sfepy.linalg import dot_sequences as dot
  from sfepy.mechanics.tensors import get_full_indices

  c = dot(cache.mtx_f, cache.mtx_f, 'ATB')
  e = 0.5 * (c - nm.eye(3))

  ii = get_full_indices(3)
  c2 = cache.sym_c[..., ii, 0]
  e2 = cache.green_strain[..., ii, 0]

  assert(nm.allclose(nm.sqrt(i3), cache.det_f, rtol=1e-15, atol=1e-15))
  assert(nm.allclose(c, c2, rtol=1e-15, atol=1e-15))
  assert(nm.allclose(e, e2, rtol=1e-15, atol=1e-15))

The last line assertion fails, so the Green strain e2 as computed by the dw_tl_he_neohook term call differs from e computed by definition (0.5 * (F^T F

• I)).

It has escaped me for so long as we have used the green strain only in postprocessing to make "colorful images"... The Green strain has not been used in any further computations. The stresses are ok - they are computed from the C invariants directly.

The problem (doubled out-of diagonal entries of E) is now fixed in the repo and your example gives positive i3 in all time steps.

Thanks again for noticing the problem!

Cheers, r.

PS: If you would like to have a term/terms for all the attributes of the evaluate cache above (do 'print cache' to see them), add an issue, please.

...

Hello Robert! I got a question about the energy calculation again :)

If you remember, in my programm there is function get_Wh that is called in postproc. This function compute the determinant of the right Cauchy-Green deformation tensor. When I was trying to do a large deformation, a situation arose, where in some cells the determinant is very small or even negative.

I can analyze the results on these elements in Paraview, so I see that

On 11/06/2013 08:45 AM, Anastasia Konovalova wrote: the

...

field of displacements of these cells are normal. I can deform my sample by displacement, so I find out that the volume of element is normal too, determinant haven't been far from 1. But If I calculate the determinant from the components of strain tensor by hands, I'll get this negative value, so that the computation of the determinant is right too.

It seems to me that this is the problem of the Green strain tensor computation.

I attached the screenshot from Paraview, where you can see the determinant value, the volume of element, and components of the Green strain tensor, the file of programm and a simple mesh, and file with the results (for paraview or some other similar programm) of one of the first steps, when the negative determinant appears.

At the function get_Wh I get the the Green strain tensor, compute the right Cauchy-Green deformation tensor (C = 2E+I), and get i3 = nm.linalg.det(C). I need the sqrt of i3 to get a J = dV/dV_0, and the error appears there.

Perhaps, it's too difficult to understand all this, so I will be glad to any advices. Thank you anyway.