Improvement of contact-friction solver

by M. Abbas, EDF R&D / AMA

This work is a deliverable of the project Advanced Numerical Methods in Mechanics, in partnership with the Laboratory of Mechanics and Acoustics from Marseilles (CNRS Research Unit).

In recent months, thanks to the PhD work of A.D. Kudawoo, performance of the contact-friction solver in Code_Aster has greatly improved. The introduction of a generalized Newton algorithm has allowed spectacular gains in computational time. This method, however, is less robust than the "traditional" methods and often requires to tweak numerical parameters (the augmentation coefficients in the first place), especially in the case of simulations involving friction.

This lack of robustness leads to the appearance of cycling between the different contact statutes during the convergence of the Newton algorithm (contact/no contact, stick/slip, forward slip/backward slip). These cycles are automatically detected by Code_Aster.

Up to now, this detection only served as a warning to the user for those difficult cases, where an adaptation of the augmentation coefficient was necessary or resorting to a less efficient but more robust method (fixed point algorithm) was advised.

From now on, a new heuristic implemented in Code_Aster enables to automatically adapt the numerical coefficients and thus reduces the number of cycles.

In order to enable this automatic process, one needs to use the keyword ADAPT_COEF=’OUI’ in DEFI_CONTACT. This method does not change the accuracy of the results but allows faster convergence.

Improved robustness

To make it converge, the test-case ssnv128r, which uses the algorithm of generalized Newton, requires a value of the augmentation coefficient, COEF_FROT equal to 1.0E6. This optimal coefficient was found through a thorough parametric study. With the automatic adjustment method enabled in this test-case, the generalized Newton algorithm converges with the default parameter COEF_FROT = 100, the algorithm indeed finds an optimal value which is not far from the one found by the parametric study.

Improved performance

The test-case ssnv209a uses the POINT_FIXE method and requires 37 Newton iterations. The switch to Newton generalized fails due to a lack of convergence. After having activated the cycling correction, the test passes thereby improving performance (8 Newton iterations instead of 37).