syfi team mailing list archive

[Harish Narayanan <harish.mlists@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