Higher order Hermite enriched contact finite elements for adhesive contact problems

It is known that during the simulation of the adhesive contact problems highly nonlinear responses of interaction forces occur within the very narrow adhesive zone. It leads to the loss of quadratic-rate of convergence during Newton-Raphson iterations and unstable computational behaviour. In case of standard finite element formulation, a very fine mesh resolution is needed for the stable computations, but a significant computational cost is associated. For minimising the cost without the loss of accuracy of the solution, contact surface enrichment approaches have been presented. These approaches utilise the higher-order Lagrangian polynomial functions for the enrichment of contact finite elements. In the present work, based on the incorporation of fifth- and seventh-order Hermite interpolation functions two new enriched contact finite elements are formulated. The performance of proposed enriched contact finite elements is demonstrated through the simulation of peeling of an initially flat deformable strip from a rigid substrate. A stable solution is obtained at a relatively coarser mesh than the fully Lagrangian discretised finite element mesh. It is shown that the proposed higher order Hermite enriched contact finite elements attain better performance when compared with earlier introduced enriched elements.