Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding

• Extends isogeometric enrichment for finite elements to 3D mixed-mode contact.
• Produces at least C1C1 continuity on the contact surface without smoothing techniques.
• Provides higher-order evaluation of surface integrals.
• Simplifies generation of volumetric meshes from IGA surface representations.
• Achieves high accuracy and increases robustness compared to Lagrangian finite elements.

We present an isogeometric enrichment technique for three-dimensional finite element computations applied to frictional contact and mixed-mode debonding. This is an extension of previous work that focused on two-dimensional and frictionless problems. To offer a more complete view of the enriched element’s performance, a comparison of the results to tri-variate isogeometric discretizations and standard Lagrangian elements is also included here. The enrichment is applied by discretizing parts of the surface that require higher accuracy with isogeometric basis functions, while the rest of the body uses Lagrangian shape functions. By using an isogeometric surface representation, the higher continuity across element boundaries and higher order of interpolation can be exploited. At the same time, the generation of tri-variate isogeometric meshes is avoided.A convergence study without any surface effects, involving only volume integrals, shows that the enriched elements can also be beneficial for these problems. The major advantage of the isogeometric element enrichment over standard tri-linear elements is demonstrated in contact problems including normal and tangential tractions. For both, mixed-mode cohesive debonding and frictional contact, the enrichment increases robustness and leads to more accurate results than standard linear Lagrangian elements. All computations are also compared to results using tri-variate isogeometric discretizations to give a complete picture of the element’s performance. It is also shown that the proposed enrichment formulation has advantages in mesh generation.