Finite strain rotations

[tophmatthews]

Hi All,

I have a question about finite strain rotations, specifically perform_finite_strain_rotations in ADComputeMultipleInelasticStress. When should perform_finite_strain_rotations be true (or conversely false). Trying to read around a bit, it looks like you don't need to do the rotations if everything is small strains...but what does that mean? Can I get away from the rotations if I am only dealing with things growing or shrinking, and not rotating?

I ask because first, it can be a bit expensive doing so many tensor operations in AD. Also, and maybe more concerning, is the stress calculation in ADComputeMultipleInelasticStress vs "stress update" classes, such as ADRadialReturnStressUpdate derivatives. In ADComputeMultipleInelasticStress, the stress is calculated:

  if (_is_elasticity_tensor_guaranteed_isotropic || !_perform_finite_strain_rotations)
    _stress[_qp] = _elasticity_tensor[_qp] * (_elastic_strain_old[_qp] + elastic_strain_increment);
  else
    _stress[_qp] = _stress_old[_qp] + _elasticity_tensor[_qp] * elastic_strain_increment;

While in ADRadialReturnStressUpdate, the stress is calculated:

// Use the old elastic strain here because we require tensors used by this class
// to be isotropic and this method natively allows for changing in time
// elasticity tensors
stress_new = elasticity_tensor * (elastic_strain_old + strain_increment);

Alright, makes sense using the ADRadialReturnStressUpdate technique since I typically use an evolving elasticity tensor, but won't this lead to a mismatch in stress calculations when perform_finite_strain_rotations=false?

I guess the question is, when should I not do perform_finite_strain_rotations=false. Maybe looking at the TM pros @bwspenc @sapitts @jiangwen84...

Thanks!

-Topher

[jiangwen84]

Since @recuero has been working on this recently, he might be able to give more details.

[recuero]

@tophmatthews My two cents below. I do not know much about the history of these classes though...

Can I get away from the rotations if I am only dealing with things growing or shrinking, and not rotating?

Maybe. I believe you are suggesting mixing small and large strain kinematic descriptions, i.e. the rotation matrix being unity. This solution would require having prior knowledge that the system does not rotate in any part of it (not just rigid body rotations), which may happen in very particular cases.

Alright, makes sense using the ADRadialReturnStressUpdate technique since I typically use an evolving elasticity tensor, but won't this lead to a mismatch in stress calculations when perform_finite_strain_rotations=false?

Doesn't ADRadialReturnStressUpdate override the calculation of stresses in ADComputeMultipleInelasticStress? I think I don't understand.

when should I not do perform_finite_strain_rotations=false

I would choose perform_finite_strain_rotations=true any time you have large deformation kinematics. Those transformations appear necessary for that application. True, AD tensor operations are a significant drag, but choosing, in general, to disregard rotations for large deformations seems like could lead to erroneous results.

Others can chime in with more accurate explanations.

[recuero]

Yeah, so rigid body rotations happen if F = RU, for U = identity (other issues such as correct BCs would come into play here for most of our static simulations). In general, R (rotation matrix) is needed to capture the local change of orientation. So, it's not so much a mesh rotating, but the result of applying locally (integration point wise) the polar decomposition. You could have drastic changes of orientation without rigid body modes.

[srinath-chakravarthy]

Here is a decent example of why we need to do rotations when using the cauchy stress, this is from abaqus theory manual. Note moose uses a variant of the Hughes widget algorithm for computing the strains (Rashid 1993) i think

https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm?startat=ch03s02ath60.html

[tophmatthews]

Okay great, so I need them. I also misread the code, and indeed the stress calculations are consistent due to _is_elasticity_tensor_guaranteed_isotropic being true.

[sapitts]

@WilkAndy and I discussed this issue in detail a few years back on one of his pull requests (I think on one of the Cosserat PRs), but I haven't been able to find that PR and discussion yet. Once I do I'll post a link here for completeness.

[WilkAndy]

Hi @sapitts . It might have been #9438 . It's fun to read these old discussions. Anyway, i concur with what's been written above