Computational Mechanics

, Volume 63, Issue 6, pp 1091–1110 | Cite as

Nitsche’s method for finite deformation thermomechanical contact problems

  • Alexander SeitzEmail author
  • Wolfgang A. Wall
  • Alexander Popp
Original Paper


This paper presents an extension of Nitsche’s method to finite deformation thermomechanical contact problems including friction. The mechanical contact constraints, i.e. non-penetration and Coulomb’s law of friction, are introduced into the weak form using a stabilizing consistent penalty term. The required penalty parameter is estimated with local generalized eigenvalue problems, based on which an additional harmonic weighting of the boundary traction is introduced. A special focus is put on the enforcement of the thermal constraints at the contact interface, namely heat conduction and frictional heating. Two numerical methods to introduce these effects are presented, a substitution method as well as a Nitsche-type approach. Numerical experiments range from two-dimensional frictionless thermo-elastic problems demonstrating optimal convergence rates to three-dimensional thermo-elasto-plastic problems including friction.


Finite deformation contact Frictional contact Thermo-structure-interaction Nitsche’s method 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Seitz
    • 1
    Email author
  • Wolfgang A. Wall
    • 1
  • Alexander Popp
    • 2
  1. 1.Institute for Computational MechanicsTechnical University of MunichGarchning b. MünchenGermany
  2. 2.Institute for Mathematics and Computer-Based SimulationUniversity of the Bundeswehr MunichNeubibergGermany

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