Evaluating the performance of enriched finite elements for Hertzian contact problem

Abstract

Solution of contact problems in the field of mechanics is often very challenging, as it is hard to predict the contact forces and stresses due to non-constant boundary conditions. It is observed that when standard finite elements of linear order are used to represent the contact boundary, it is difficult to capture the contact forces within the contact region accurately. To improve this situation, different techniques usually are adopted. One such technique is using highly refined mesh at the contact zone. But it increases the computational time. Thus, it is more efficient to adopt the enrichment strategies for the contact elements lying within the contact region. Such elements are also referred to as the enriched contact finite elements. To the best of the authors' knowledge, the effects of contact enrichment with various interpolation orders on the solution accuracy of contact problems have not been exploited completely and hence is the scope for the present work. The current contribution evaluates the performance of enriched finite elements in solving the Hertz contact problem. The enrichment strategy is based on the introduction of extra degrees of freedom for the contact elements in the slave surface. The contact surface is locally enriched to represent the surface more accurately than the bulk. Thus, the improved computational contact formulation helps to correctly approximate the contact forces while keeping the total degrees of freedom low. In this work, the penalty method enforces contact constraints, and material behaviour follows the Neo-Hookean hyperelastic material model. A benchmark problem on the Hertzian contact is considered to demonstrate the FE enrichment technique. The numerical results exhibit the better performance of the FE enrichment over the mesh refinement for the solution accuracy. This work also shows that the higher-order finite elements after enrichment outperform the linear order finite elements in the contact region.