Hierarchical NURBS in frictionless contact

• Novel isogeometric contact algorithms are introduced based on hierarchical NURBS.
• Hierarchical mortar discretizations are derived for frictionless contact.
• The partition of unity property is explored for the construction of the mortar basis.
• Exterior and interior point methods are applied in regularized and exact settings.
• Full or lumped recovery approach is employed to define the kinematic mortar variable.

This work investigates mortar-based frictionless contact in the context of NURBS discretizations that are subjected to local hierarchical refinement. The investigations emphasize three sets of choices which lead to different contact algorithms that have distinct advantages and disadvantages. First, on the optimization side, both exterior and interior point methods are applied, thus spanning inexact constraint enforcement algorithms of the penalty or barrier type as well as exact ones of the primal–dual type. Second, on the discretization side, the hierarchical basis set of the mortar variables is inherited either directly from the discretization of the slave surface or after an intermediate normalization step to satisfy the partition of unity. Third, in interaction with both optimization and discretization, the kinematic mortar variable is recovered from the actual normal gap through the full or lumped solution of a linear system of equations. The implications of different choices are highlighted through benchmark problems which monitor the solution quality at the global level through the structural force evolution and at the local level through the contact pressure distribution.