Jordan Journal of Civil Engineering

Extension of the Enriched Discontinuous Galerkin Approach for Frictional Contact Involving Non-conforming Meshes with Plasticity


Layla K. Amaireh; Ghadir A. Haikal;


The Enriched Discontinuous Galerkin Approach (EDGA) is typically implemented to solve the continuity problem at the interface of contact problems involving non-conforming meshes (NCMs). Through local enrichment, the EDGA enables a two-pass strategy for the enforcement of geometric compatibility at all nodes of the interface without the need of a master-slave definition. The local enrichment transforms the geometric compatibility condition to a set of node-to-node constraints by inserting a new node where a node meets a surface. Updating the set of Lagrangian shape functions to account for the additional node ensures the completeness of the finite element interpolation in the enriched element. In this study, the EDGA is extended to model large-deformation contact problems between bodies with plasticity. However, the enrichment introduces higher-order element shape functions associated with the interface nodes. To solve this problem without losing the material history at the existing integration points, Gauss-Kronrod method for numerical integration is utilized to add an additional set of integration points interlaced between the original Gaussian quadrature. Material history at the additional integration points is then interpolated from the existing points. After proper formulations that pass the contact patch test, this study, through various cases with and without plasticity, confirmed the necessity for proper treatment of contact problems to accurately capture the tractions transferred through the interface between two bodies. Without proper treatment, the results are not accurate, especially for critical contact problems, such as football helmet-skull interaction and oil pipe-soil interaction.


Galerkin approach, Contact formulation, Non-conforming meshes, Plasticity