[Libmesh-devel] Candidate for systems_of_equations_ex7: nonlinear elasticity

[David K. <dav...@ak...>]

Hi all,

There have been several questions on the mailing list about nonlinear
elasticity, so I wanted to provide a new example (systems_of_equations_ex7)
that addresses this. Note that fem_system_ex2 is a neo-Hookean model, but I
think it's quite complicated, so I think a simpler nonlinear elasticity
example would be helpful for users.

I have attached an implementation of a St. Venant-Kirchoff cantilever beam,
i.e. similar to systems_of_equations_ex6 except that it allows for large
deformation (nonlinear strain). This implementation uses
NonlinearImplicitSystem.

The code converges and seems to give reasonable results, but I was hoping
to get a second (or more!) set of eyes on this to check that it's
reasonable. In particular, the convergence seems to be flaky if I increase
forcing_magnitude, which makes me suspect that something is wrong...

Note also that for testing purposes I recommend using a direct solver
("./example-opt -ksp_type preonly -pc_type lu") so that you don't have to
worry about iterative solver convergence (this example is small so LU is
fast enough).

If anyone is available/interested to look over this example in more detail,
please do let me know.

Thanks,
David