Hello everyone.
Is there anyone here with hands-on experience at the implementation the Augmented Lagrangian method of contact analysis in 2D and 3D?
I know the theory and the basics and I have implemented the method in 2D and 3D. My issue is with the convergence of the method specially in 3D and when the contact has friction. I have read some papers but they don't help. I am looking forward to hearing be practical tips.
There are many implementations of deformable-rigid and deformable-deformable contact based on the augmented Lagrangian method, available. I guess you have read Wrigger's computational contact mechanics bible. When it comes to Coulomb friction, there is no guaranteed unique solution for large values of the friction coefficient but for small values like 0.1-0.3, you shouldn't in general experience severe convergence issues. Independent of the presence of friction, it helps in general to use some kind of line-search in your Newton loop. The value of the augmentation parameter can also affect convergence, but there is normally a wide range of values that work well, see the parametric studies in
Article Generalized Newton’s methods for the approximation and resol...
There is also a difference if you implement the method in a nodal sense or in an integral sense, i.e. at Gauss points. If you want to read about our integral implementation of augmented Lagrangian deformable-deformable contact in GetFEM I can recommend you our paper:
Article An unconstrained integral approximation of large sliding fri...
The code of this implementation is also available. You can e.g. find parts of it if you look at the intergral_large_sliding_contact_brick_raytracing class in the file
http://git.savannah.nongnu.org/cgit/getfem.git/tree/src/getfem_contact_and_friction_large_sliding.cc
Thank you very much for the reply and for the papers.
My implementation is in nodal sense and the scope is limited to small strain.
In practice I have faced many challenges that may not be discussed in papers. There are models in which some of the slave nodes oscillate between contacting and separation. An example is attached. The magnets are trapped in the pocket and a detection failure in one iteration could cause the magnets fly away. Such cases pose challenges even without considering friction but with friction the failure could be more catastrophic.
I have also faced a more fundamental issue related to ALM which could occur even in simple models. When the 1st augmentation loop completes and the 2nd one starts, the sum of the augmentation and penalty forces could simply become too much and , instead of reducing the penetration to near zero, it could cause a gap between the master and slave, resulting in loss of contact. We can handle this by some relaxation factor in updating the Lagrange multipliers but it affects both the accuracy and efficiency.
Lagrange-based contact methods are prone to rigid body motion to enforce Hertz-Signorini-Moreau conditions. And they are more open to oscillations and convergence issues. So you can try to use Penalty contact instead of ALM. Try conforming meshes between contacting bodies, and try node to node implementation. But, most probably, you will need relaxation for the Penalty contact as well. So please check the output file for contact convergence to be sure. If you would like to see a detailed comparison of the contact algorithms, you might be interested in the following.
Yuksel, E., Erturk, A. S., and Budak, E. (May 14, 2020). "A Hybrid Contact Implementation Framework for Finite Element Analysis and Topology Optimization of Machine Tools." ASME. J. Manuf. Sci. Eng. August 2020; 142(8): 081001. https://doi.org/10.1115/1.4046985
Esra Yuksel
Thank you very much for the helpful comment.
I am eager to study your paper.
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