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.

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.
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