A Globally Convergent Filter–trust-region Method for Large Deformation Contact Problems

We present a globally convergent method for the solution of frictionless large deformation contact problems involving hyperelastic materials. For the discretisation we apply the dual 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. This method combines several techniques from non-linear optimisation to achieve global convergence towards first-order optimal points. To speed up the method inexact linearisations of the non-penetration constraint are used whenever the current iterate is far away from a critical point. A monotone multigrid method is applied for the fast solution of the constrained Newton problems.