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

2017/08/04 by Jonathan Youett, Youett, Jonathan, Oliver Sander +3 · 1 citation
Computer Science · Engineering · #65K15 #65N55 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1708.01455

openalex publication_date 2017/08/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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

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