A finite deformation mortar contact formulation using a primal-dual active set strategy

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In recent years, nonconforming domain decomposition techniques and, in particular, the mortar method have become popular in developing new contact algorithms. Here, we present an approach for 2D frictionless multibody contact based on a mortar formulation and using a primal-dual active set strategy for contact constraint enforcement. We consider linear and higher-order (quadratic) interpolations throughout this work. So-called dual Lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation, thus avoiding an increase in system size. For this type of contact formulation, we provide a full linearization of both contact forces and normal (non-penetration) and tangential (frictionless sliding) contact constraints in the finite deformation frame. The necessity of such a linearization in order to obtain a consistent Newton scheme is demonstrated. By further interpreting the active set search as a semi-smooth Newton method, contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme. This yields a robust and highly efficient algorithm for frictionless finite deformation contact problems. Numerical examples illustrate the efficiency of our method and the high quality of results.

Original languageEnglish
Pages (from-to)1354-1391
Number of pages38
JournalInternational Journal for Numerical Methods in Engineering
Issue number11
StatePublished - 10 Sep 2009


  • Dual Lagrange multipliers
  • Finite deformations
  • Mortar finite element methods
  • Multibody contact
  • Primal-dual active set strategy


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