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 >> >> > ------------------------------------------------------------------------------ Transform Data into Opportunity. Accelerate data analysis in your applications with Intel Data Analytics Acceleration Library. Click to learn more. http://pubads.g.doubleclick.net/gampad/clk?id=278785471&iu=/4140 _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users