Isogeometric finite element enrichment for problems dominated by surface effects

This work presents a local finite element enrichment technique based on isogeometric analysis. It is accurate, robust, and efficient and is especially well suited for problems dominated by surface effects such as contact of deformable bodies or adhesion. The presented enrichment techniques combines the accuracy and smoothness achieved with isogeometric analysis with the efficiency and simplicity of classical Lagrangian finite elements. Isogeometric surface elements are used locally on the contact surface, while the rest of the surface and the volume are discretised using standard Lagrangian finite elements. This leads to higher accuracy in the evaluation of the contact integral. The geometry uses the same discretisation, leading to a smooth contact surface of at least C1-continuity with a continuous normal vector on the surface. Another advantage is that for three-dimensional problems only isogeometric surfaces are required, the volumetric mesh consists of linear Lagrange elements and can be generated with existing software. Volumetric spline generation for arbitrary geometries is avoided.The presented isogeometric enrichment technique is applied to multiple numerical examples and compared extensively to other discretisations. Benefits in accuracy and efficiency are achieved and discussed