  We present a globally convergent method for the solution of frictionless
large deformation contact problems for hyperelastic materials. The
discretisation uses the mortar method which is known to be more stable than
node-to-segment approaches. The resulting non-convex constrained minimisation
problems are solved using a filter-trust-region scheme, and we prove global
convergence towards first-order optimal points. The constrained Newton problems
are solved robustly and efficiently using a Truncated Non-smooth Newton
Multigrid (TNNMG) method with a Monotone Multigrid (MMG) linear correction
step. For this we introduce a cheap basis transformation that decouples the
contact constraints. Numerical experiments confirm the stability and efficiency
of our approach.
