  A novel adaptive local surface refinement technique based on Locally Refined
Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model
complex geometries exactly and are the rational extension of LR B-splines. The
local representation of the parameter space overcomes the drawback of
non-existent local refinement in standard NURBS-based isogeometric analysis.
For a convenient embedding into general finite element code, the B\'ezier
extraction operator for LR NURBS is formulated. An automatic remeshing
technique is presented that allows adaptive local refinement and coarsening of
LR NURBS. In this work, LR NURBS are applied to contact computations of 3D
solids and membranes. For solids, LR NURBS-enriched finite elements are used to
discretize the contact surfaces with LR NURBS finite elements, while the rest
of the body is discretized by linear Lagrange finite elements. For membranes,
the entire surface is discretized by LR NURBS. Various numerical examples are
shown, and they demonstrate the benefit of using LR NURBS: Compared to uniform
refinement, LR NURBS can achieve high accuracy at lower computational cost.
