On the coupling of local multilevel mesh refinement and ZZ methods for unilateral frictional contact problems in elastostatics

Hao Liu (1) , Isabelle Ramière (1) , Frédéric Lebon (2)

1 LSC - Laboratoire de Simulation du Comportement des Combustibles
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper addresses an efficient and robust automatic adaptive local multilevel mesh refinement strategy for unilateral frictional contact problems in elastostatics. The proposed strategy couples the Local Defect Correction multigrid method LDC (Hackbusch, 1984) with the ZZ (Zienkiewicz and Zhu, 1987) a posteriori error estimator. An extension of LDC method to frictional contact problems is introduced. An interesting feature of this extended LDC algorithm is that it still only lies on interpolations of displacement fields. Neither forces conservation nor exchange of contact status is required between the refinement levels. The ZZ a posteriori error estimator is exploited to automatically build the sub-grids of the LDC method. A criterion linked to the relative error in stress is used. The efficiency of the proposed strategy is analyzed on examples derived from nuclear engineering. Practical numerical choices are proposed and justified. The refinement process automatically varies and stops with respect to a given tolerance. Post-treatments show that the sub-grids focus around the contact areas and that the converged LDC solution always respects the prescribed tolerance.

Mots clés: Automatic adaptive mesh refinement; Multilevel local defect correction method; Zienkiewicz and Zhu a posteriori error estimator; Frictional contact problems; Signorini-Coulomb; User tolerance

Domaines: Mécanique des solides [physics.class-ph]

Hao Liu, Isabelle Ramière, Frédéric Lebon. On the coupling of local multilevel mesh refinement and ZZ methods for unilateral frictional contact problems in elastostatics. Computer Methods in Applied Mechanics and Engineering, 2017, 323, pp.1-26. ⟨10.1016/j.cma.2017.04.011⟩. ⟨hal-01694040⟩