syfi team mailing list archive

[kent-and@xxxxxxxxx]

> kent-and@xxxxxxxxx wrote:
>>> kent-and@xxxxxxxxx wrote:
>>>>> kent-and@xxxxxxxxx wrote:
>>>>>>> kent-and@xxxxxxxxx wrote:
>>>>>>>> The nonlinear hyper-elasticity demos do not seem to produce
>>>>>>>> the correct solution. I have been looking in particular on the
>>>>>>>> Fung
>>>>>>>> stuff.
>>>>>>>>
>>>>>>>> Newton seems to converge with quadratic convergence whenever
>>>>>>>> it is close to the solution so I think the differentiation is
>>>>>>>> correct.
>>>>>>> OK. I have been trying a few things over the past week (compiling
>>>>>>> forms
>>>>>>> with FFC instead) and here is what I see:
>>>>>>>
>>>>>>> 1. Nonlinear scalar Poisson works.
>>>>>>> 2. Linear elasticity posed as a special case of a nonlinear problem
>>>>>>> works. (Converges in one iteration).
>>>>>>> 3. Nonlinear elasticity (hyperelasticity with the St.
>>>>>>> Venant-Kirchhoff
>>>>>>> model) a. does not converge or b. the direct solvers complain about
>>>>>>> a
>>>>>>> singular matrix.
>>>>>>>
>>>>>>> I didn't think to look into the boundary conditions for 3 because I
>>>>>>> used
>>>>>>> the same setting as 2. I will look at them more closely.
>>>>>>>
>>>>>>> Harish
>>>>>> I don't think it is a problem with the bc. I tested some nonlinear
>>>>>> variants
>>>>>> of Poisson that come from convex functionals. In these cases Newton
>>>>>> should work. Can we say the same about SVK or Fung or do we either
>>>>>> need a relaxation scheme or start close to the solution ?
>>>>> For the SVK or Fung (or any material model) that has been correctly
>>>>> linearised, the Newton-Raphson scheme should converge quadratically
>>>>> as
>>>>> long as one starts close to the solution. In practice, this is
>>>>> ensured
>>>>> by not driving the problem too much in a given (time) step.
>>>>>
>>>>> Harish
>>>> The Newton-Raphson scheme should always converge quadratic as long as
>>>> one starts close enough to the solution :)
>>> I know :). Then I didn't understand what you meant by:
>>>
>>> I tested some nonlinear variants of Poisson that come from convex
>>> functionals. In these cases Newton should work.
>>>
>>> Did you mean, a Newton solver should work from any starting point?
>>>
>>> Harish
>>
>> Yes,  for an equation like
>> -Delta u + u**p
>>
>> where p is odd.
>
> OK, and by "work" do you mean will head in the right direction (not
> necessarily at a quadratic rate)? If that is what you meant, then this
> is true of these hyperelastic materials as well. The strain energy is a
> convex function of the deformation measure.
>
> Harish


For the above equation I think there should be only one minimum and so
it will head in the right direction. I'm not sure whether it should be
quadratic.
If it is convex it can have several minium and it may therefore head
towards different minima at different times but I didn't think it could head
off to infinity (or creating a singular matrix) ?

Kent