COMPLAS 2025

Keynote

Approximation of frictional contact using nitsche’s methods in 3d elasto-plastic industrial problems

  • Pozzolini, Cedric (FRAMATOME)

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Frictional, elasto-plastic multi-body contact problems play an important role in mechanical engineering. The non-linearities caused by geometric contact and frictional constraints, combined with the non-linearity in the material law result in challenging numerical problems in the forms of variational inequalities. Therefore efficient solving methods are needed. Numerical methods for contact problems have been an active field of research for many years but still new methods keep emerging. Probably the youngest member of the family is Nitsche’s method, see [2]. A first application to contact mechanics was presented in 1993 by P. Wriggers and G. Zavarise, and a mathematical analysis for linearized kinematics has been published [1]. Unlike any other method, Nitsche’s method is at the same time variationally consistent (and therefore optimally convergent) and does not introduce any additional degrees of freedom. This comes at the expense of having to evaluate the boundary traction from the continuum stresses. In this note, we describe the use of Nitsche’s method to prescribe a contact (with or without Coulomb friction condition) between two elasto-plastic bodies. This corresponds to a weak integral contact condition which has some similarities with the ones using Lagrange multipliers. The goal of this talk is to present how differents industrials cases in SYSTUS/SYSWELD where we used Nitsche’s methods to solve certain contact problems in the context of large deformations. The approximation strategy proposed here was implemented for the first time in the open source finite element library GetFEM for contacts in small and large elastic or hyperelastic déformations with or without friction. We will present some comparison with penalty or augmented lagrangian methods, for segment-to-segment, point-to-point or node-to-node strategies.