Massively Parallel Simulation and Adaptive Mesh Refinement for 3D Elastostatics Contact Mechanics Problems

Abstract

The numerical simulation of contact mechanics problems is computationally challenging, as these problems are locally highly non-linear and non-regular. Efficient numerical solutions of such problems usually rely on adaptive mesh refinement (AMR). Even if efficient parallelizations of standard AMR techniques as h-adaptive methods begin to appear [1], their combination with contact mechanics problems remains a challenging task. Indeed, current developments on algorithms for contact mechanics problems are focusing either on non-parallelized new adaptive mesh refinement methods [2] or on parallelization methods for uniform refinement meshes [3,4]. The purpose of this work is to introduce a High Performance Computing strategy for solving 3D contact elastostatics problems with AMR on hexahedral elements. The contact is treated by a node-to-node algorithm with a penalization technique in order to deal with primal variables only. Therefore, this algorithm presents the advantages of well modelling the studied phenomenon while not increasing the number of unknowns and not modifying the formulation in an intrusive manner. Concerning the AMR strategy, we rely on a non-conforming h-adaptive refinement solution. This method has already shown to be well scalable [1,7]. Regarding the detection of the refinement zones, a Zienkiewicz-Zhu (ZZ) type error estimator is used to select the elements to be refined through a local detection criterion [5]. In addition, a geometric-based stopping criterion is applied in order to automatically stop the refinement process, even in case of local singularities. This combined strategy has recently proven its efficiency [6]. In this contribution, we endeavor to extend the combination of these contact mechanics and AMR strategies to a parallel framework. In order to carry