On Wed, Mar 30, 2016 at 2:31 PM, David Knezevic <david.kneze...@akselos.com>
wrote:

> Paul, FYI, I think I've figured out what's going on here.
>
> If the whole model is in the elastic regime, then the analytical and f.d.
> jacobians match.
>
> If I set the load to be sufficiently high such that the entire model is
> plastic, then again the analytical and f.d. jacobians match.
>
> The case where I get a mismatch is if the model is part elastic and part
> plastic. In this case, I believe that the finite difference jacobian is
> wrong because the small f.d. perturbations can lead to a change from
> elastic to plastic (or vice versa), which leads to a large error in the
> jacobian. Does that sound like a plausible explanation to you?
>


P.S. Actually, there's also another issue that I think is more significant.
In order to implement radial return according to the algorithm in Simo &
Hughes, I store material data (e.g. plastic strain) at each quadrature
point "qp". But the finite difference jacobian does solves at "qp + h" ,
and when it does those perturbed solves it uses the material data from
"qp", which is not correct.

Based on my tests, I believe this is the real source of the mismatch
between the f.d. and analytical jacobian. (The effect I mentioned in my
previous email may be an issue too, but I think it's less significant.)

David


On Wed, Mar 30, 2016 at 9:25 AM, David Knezevic <david.kneze...@akselos.com>
> wrote:
>
>> On Wed, Mar 30, 2016 at 9:20 AM, Paul T. Bauman <ptbau...@gmail.com>
>> wrote:
>>
>>>
>>>
>>> On Wed, Mar 30, 2016 at 9:16 AM, David Knezevic <
>>> david.kneze...@akselos.com> wrote:
>>>
>>>> On Wed, Mar 30, 2016 at 9:11 AM, Paul T. Bauman <ptbau...@gmail.com>
>>>> wrote:
>>>>
>>>>>
>>>>>
>>>>> On Wed, Mar 30, 2016 at 8:00 AM, David Knezevic <
>>>>> david.kneze...@akselos.com> wrote:
>>>>>>
>>>>>>
>>>>>> Thanks for your comments. The problem I'm considering is plasticity,
>>>>>> using the radial return algorithm. As far as I can tell, the code matches
>>>>>> the text book, and it converges correctly. However, it doesn't match the
>>>>>> finite difference Jacobian from FEMSystem. So there are two 
>>>>>> possibilities:
>>>>>>
>>>>>> 1) Somehow the finite difference Jacobian is inconsistent with the
>>>>>> radial return algorithm. This doesn't seem impossible to me, given that 
>>>>>> the
>>>>>> radial return algorithm is highly path-dependent.
>>>>>>
>>>>>
>>>>> This is very much a thing. What reference are you using? The Jacobian
>>>>> you get from the equations vs. the Jacobian which includes the radial
>>>>> return algorithm ("consistent tangent" as the community calls it) are
>>>>> different. Simo and Hughes, "Computationally Inelasticity" has a good
>>>>> discussion of this.
>>>>>
>>>>
>>>>
>>>> I'm using Simo and Hughes. I implemented the algorithm in "Box 3.2" of
>>>> that book for radial return, and it seems to be working fine.
>>>>
>>>
>>> OK, cool. Just wanted to make sure you were aware (I figured you were).
>>>
>>>
>>>> However, I would have thought that I could use a finite difference
>>>> Jacobian based on the residual that is given by the radial return algorithm
>>>> (i.e. the residual that uses the stress from radial return). I would have
>>>> thought that yields a "consistent tangent", no?
>>>>
>>>
>>> Agreed. I'd suspect a bug, or I'm forgetting something because I haven't
>>> played with damage/plasticity in ~3 years.
>>>
>>
>>
>> OK. I was hoping there might be some reason that the finite difference
>> could be wrong in this case... but I agree, it's more likely that there's
>> just a bug.
>>
>> Do you get dramatic convergence behavior changes between the finite
>>> difference version and the analytical version? If not, very likely there's
>>> some small term that's missing/in error.
>>>
>>
>> They both converge similarly, so yeah, there's probably a small term
>> that's in error.
>>
>> Thanks,
>> David
>>
>>
>
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