Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 36))

  • 133 Accesses

Abstract

We describe non-penetration conditions using biorthogonal mortars, proving that the constraint matrices arising from the discretization by some biorthogonal bases are well-conditioned and show that the procedure complies well with the domain decomposition method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Wohlmuth, B.I.: Discretization Methods and Iterative Solvers Based on Domain Decomposition. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  2. Wohlmuth, B.I.: Variationally consistent discretization scheme and numerical algorithms for contact problems. Acta Numer. 20, 569–734 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Popp, A., Seitza, A., Geeb, M.W., Wall, W.A.: Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach. Comput. Methods Appl. Mech. Eng. 264, 67–80 (2013)

    Article  MathSciNet  Google Scholar 

  4. Vlach, O., Dostál, Z., Kozubek, T.: On conditioning the constraints arising from variationally consistent discretization of contact problems and duality based solvers. Comput. Methods Appl. Math. 15(2), 221–231 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kozubek, T., Markopoulos, A., Brzobohatý, T., Kučera, R., Vondrák, V., Dostál, Z.: MatSol–MATLAB efficient solvers for problems in engineering. The library is no longer updated and is replaced by the ESPRESO framework. http://numbox.it4i.cz

  6. Maday, Y., Mavriplis, C., Patera, A.T.: Nonconforming mortar element methods: application to spectral discretizations. In: Chan, T. (ed.) Domain Decomposition Methods, pp. 392–418. SIAM, Philadelphia (1989)

    MATH  Google Scholar 

  7. Puso, M.: A 3D mortar method for solid mechanics. Int. J. Numer. Methods Eng. 59, 315–336 (2004)

    Article  MATH  Google Scholar 

  8. Puso, M., Laursen, T.: A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Eng. 193, 601–629 (2004)

    Article  MATH  Google Scholar 

  9. Wriggers, P.: Contact Mechanics. Springer, Berlin (2005)

    MATH  Google Scholar 

  10. Dickopf, T., Krause, R.: Efficient simulation of multibody contact problems on contact geometries: a flexible decomposition approach using constrained optimization. Int. J. Numer. Methods Eng. 77(13), 1834–1862 (2009)

    Article  MATH  Google Scholar 

  11. Chernov, A., Maischak, M., Stephan, E.P.: hp-mortar boundary element method for two-body contact problems with friction. Math. Methods Appl. Sci. 31, 2029–2054 (2008)

    Google Scholar 

  12. Wohlmuth, B.I., Krause, R.: Monotone methods on nonmatching grids for nonlinear contact problems. SIAM J. Sci. Comput. 25, 324–347 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dostál, Z., Vlach, O., Brzobohatý, T.: Scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions. Finite Elem. Anal. Des. 156, 34–43 (2019)

    Article  MathSciNet  Google Scholar 

  14. Dostál, Z., Vlach, O.: An accelerated augmented Lagrangian algorithm with adaptive orthogonalization strategy for bound and equality constrained quadratic programming and its application to large-scale contact problems of elasticity. J. Comput. Appl. Math. 394, 113565 (2021)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zdeněk Dostál .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Dostál, Z., Kozubek, T. (2023). Mortars. In: Scalable Algorithms for Contact Problems. Advances in Mechanics and Mathematics, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-33580-8_16

Download citation

Publish with us

Policies and ethics

Navigation