NURBS-enriched contact finite elements

摘要

A novel enrichment of finite elements for contact computations based on isogeometric analysis is presented. Each body is divided into two parts, an enriched contact surface and the bulk domain together with surfaces that are not in contact. The latter part comprises the large majority of the domain and is treated in the usual manner with standard linear basis function, preserving the efficiency of classical finite element techniques. The enriched contact surface is discretized using NURBS basis functions of at least second order, allowing for a locally differentiable surface representation. This avoids the problem of suddenly changing normal vectors between element boundaries on the contact surface. Following the concept of isogeometric analysis, the smooth basis functions are not only used to describe the surface geometry, but also to approximate the solution on the surface. This leads to higher accuracy in the contact integral evaluation. Numerical results are presented for 2D and 3D contact computations including frictionless sliding, adhesive peeling, and cohesive debonding. The presented contact element enrichment exhibits a major gain in numerical accuracy and stability without loss of efficiency compared to standard linear finite elements. The enrichment technique offers some advantages over Hermite and higher-order Lagrangian contact element enrichment techniques, such as locally differentiable surface representations in 3D, while featuring competitive accuracy and performance.