A globally convergent filter-trust-region method for large deformation contact problems

TL;DR

This paper introduces a globally convergent filter-trust-region method for solving large deformation contact problems in hyperelastic materials, utilizing mortar discretisation and a TNNMG solver for efficiency.

Contribution

It presents a novel combination of mortar discretisation with a filter-trust-region scheme and TNNMG solver, ensuring global convergence and computational robustness.

Findings

Method is stable and efficient in numerical experiments.

Proves global convergence towards first-order optimal points.

Decouples contact constraints with a new basis transformation.

Abstract

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.