Self-contact only — Issue with augmented Lagrangian method

General
1

Dear all,

I am currently working on a self-contact problem in large deformation elasticity using the augmented Lagrangian method in GetFEM++.

I’ve designed my code in a modular way so that it can be extended later not only to handle self-contact but also contact between multiple bodies .

While the approach works in some cases, it fails in others — for instance, the contact is not properly detected, or the solver becomes unstable or fails to converge.
I’ve experimented with several parameters, including:

  • the augmented Lagrangian parameter ,
  • the realised distance threshold ,
  • and other factors such as mesh refinement and initial configurations .
    Despite this, I still can’t identify the root cause of the failures.

Below is an excerpt of the code responsible for the contact implementation.
I would greatly appreciate it if you could take a look and let me know if anything seems incorrect or poorly defined.

Thank you in advance for your help and time.

Best regards,

    md1.add_raytracing_transformation("raytrace", release_dist)
    md1.define_variable_group("u_r", "u") # can be extend for u1, u2, u3 etc ...
    md1.add_master_contact_boundary_to_raytracing_transformation("raytrace", m, "u_r", 911) 
    md1.add_nonlinear_term(mim_contact2, "-contact_mult2.Test_u", 911) 
    md1.add_nonlinear_term(mim_contact2, "-(1/c)*contact_mult2.Test_contact_mult2", 911) 
    md1.add_macro("normal2", "Normalized(Inv(F1').Normal)")
    md1.add_macro("gap2", "(Interpolate(X,raytrace)+Interpolate(u_r,raytrace)-X-u).normal2")
    md1.add_nonlinear_term(mim_contact2,
        "Interpolate_filter(raytrace,(-1/c)*neg_part(contact_mult2.normal2+c*gap2)*normal2.Test_contact_mult2, 1)", 911) 
    md1.add_nonlinear_term(mim_contact2,
                        "Interpolate_filter(raytrace, -neg_part(contact_mult2.normal2+c*gap2)*normal2.Interpolate(Test_u,raytrace), 1)",
                        911)
2

To get a robust contact formulation that works in all cases is very difficult. Commercial programs use a lot of heuristics and special treatment of corner cases.

One strategy is to start with an imprecise penalized contact formulation (i.e. with a low penalty parameter) which is quite robust. Then you can use the solution from the imprecise model as a start guess for your precise model with the augmented lagrangian formulation.

1 Like
3

Dear @Konstantinos.Poulios

Thank you so much for your advice, I’ll implement and let you know.

Best