Skip to main content
SpringerLink
Log in

Coupling Fluid-Structure Interaction with Phase-Field Fracture: Modeling and a Numerical Example

  • Conference paper
  • First Online:
Numerical Mathematics and Advanced Applications ENUMATH 2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 112))

Abstract

In this work, a framework for coupling arbitrary Lagrangian-Eulerian fluid-structure interaction with phase-field fracture is suggested. The key idea is based on applying the weak form of phase-field fracture, including a crack irreversibility constraint, to the nonlinear coupled system of Navier-Stokes and elasticity. The resulting setting is formulated via variational-monolithic coupling and has four unknowns: velocities, displacements, pressure, and a phase-field variable. The inequality constraint is imposed through penalization using an augmented Lagrangian algorithm. The nonlinear problem is solved with Newton’s method. The framework is tested in terms of a numerical example in which computational stability is demonstrated by evaluating goal functionals on different spatial meshes.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. W. Bangerth, R. Hartmann, G. Kanschat, Deal.II – a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33 (4), 24/1–24/27 (2007)

    Google Scholar 

  2. M.J. Borden, C.V. Verhoosel, M.A. Scott, T.J.R. Hughes, C.M. Landis, A phase-field description of dynamic brittle fracture. Comput. Methods Appl. Mech. Eng. 217, 77–95 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. B. Bourdin, Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces Free Bound. 9, 411–430 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Bourdin, G. Francfort, J.-J. Marigo, Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48 (4), 797–826 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Bourdin, G. Francfort, J.-J. Marigo, The variational approach to fracture. J. Elast. 91 (1–3), 1–148 (2008)

    MathSciNet  MATH  Google Scholar 

  6. B. Bourdin, C. Larsen, C. Richardson, A time-discrete model for dynamic fracture based on crack regularization. Int. J. Frac. 168 (2), 133–143 (2011)

    Article  MATH  Google Scholar 

  7. T.A. Davis, I.S. Duff, An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J. Matrix Anal. Appl. 18 (1), 140–158 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Donea, S. Giuliani, J. Halleux, An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions. Comput. Methods Appl. Mech. Eng. 33, 689–723 (1982)

    Article  MATH  Google Scholar 

  9. G. Francfort, J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (8), 1319–1342 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Heister, M.F. Wheeler, T. Wick, A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach. Comput. Methods Appl. Mech. Eng. 290, 466–495 (2015)

    Article  MathSciNet  Google Scholar 

  11. J.G. Heywood, R. Rannacher, S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 22, 325–352 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Hron, S. Turek, A monolithic FEM/multigrid solver for an ALE formulation of fluid-structure interaction with applications in biomechanics, in Fluid-Structure Interaction: Modelling, Simulation, Optimisation, ed. by H.-J. Bungartz, M. Schfer (Springer, Berlin/Heidelberg, 2006), pp. 146–170

    Chapter  Google Scholar 

  13. T. Hughes, W. Liu, T. Zimmermann, Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29, 329–349 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  14. C.J. Larsen, C. Ortner, E. Süli, Existence of solutions to a regularized model of dynamics fracture. Methods Appl. Sci. 20, 1021–1048 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. Int. J. Numer. Methods Eng. 83, 1273–1311 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Mikelić, M.F. Wheeler, T. Wick, A quasi-static phase-field approach to pressurized fractures. Nonlinearity 28 (5), 1371–1399 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Richter, T. Wick, On time discretizations of fluid-structure interactions, in Multiple Shooting and Time Domain Decomposition Methods, ed. by T. Carraro, M. Geiger, S. Körkel, R. Rannacher. Contributions in Mathematical and Computational Science (Springer, 2015), pp. 377–400, http://www.springer.com/us/book/9783319233208

  18. M. Wheeler, T. Wick, W. Wollner, An augmented-Lagangrian method for the phase-field approach for pressurized fractures. Comput. Methods Appl. Mech. Eng. 271, 69–85 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. T. Wick, Fluid-structure interactions using different mesh motion techniques. Comput. Struct. 89 (13–14), 1456–1467 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RICAM, Austrian Academy of Sciences, Altenberger Str. 69, 4040, Linz, Austria

    Thomas Wick

Authors
  1. Thomas Wick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Wick .

Editor information

Editors and Affiliations

  1. Mathematics & Applied Mathematics, Middle East Technical University Mathematics & Applied Mathematics, Ankara, Turkey

    Bülent Karasözen

  2. Dept of Computer Engg, Middle East Technical Univ Dept of Computer Engg, Cankaya, Ankara, Turkey

    Murat ManguoÄŸlu

  3. Middle East Technical University Mathematics & Institute of Applied Mathe, Ankara, Turkey

    Münevver Tezer-Sezgin

  4. Civil Engineering & Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Serdar Göktepe

  5. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Turkey

    Ömür Uğur

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Wick, T. (2016). Coupling Fluid-Structure Interaction with Phase-Field Fracture: Modeling and a Numerical Example. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_38

Download citation

Publish with us

Policies and ethics

Search

Navigation