Skip to main content

Simulation of Wave Propagation and Impact Damage in Brittle Materials Using Peridynamics

  • Chapter

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 105))

Abstract

In this paper we present the results of simulating wave propagation and impact damage in brittle materials, like ceramics, using peridynamics, a non-local generalization of continuum mechanics. Two different bond-based material models, the prototype microelastic material model and its improved version, were used to model aluminum oxynitride (ALON). To validate the simulations, the speed of the wave front is compared with measured data of the edge-on impact (EOI) experiment. The presented simulation results indicate that convergence is attained, however, a modeling error of 10 % remains. Which indicates that simple bond-based peridynamics models may not be sufficient to achieve sufficient accuracy in these applications, but more sophisticated state-based peridynamics models must be employed.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
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

Learn about institutional subscriptions

Notes

  1. 1.

    Note that we assume isotropic material behavior due to the fact that s depends on \(\vert \vert \xi \vert \vert\).

References

  1. Benson, D.J.: Computational methods in lagrangian and eulerian hydrocodes. Comput. Methods Appl. Mech. Eng. 99(2–3), 235–394 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bobaru, F., Hu, W.: The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials. Int. J. Fract. 176(2), 215–222 (2012). doi:10.1007/s10704-012-9725-z. http://dx.doi.org/10.1007/s10704-012-9725-z

  3. Brannon, R., Fossum, A., Strack, E.: Kayenta: Theory and User’s Guide. Tech. Rep. SAND2009-2282, Sandia National Laboratories, Albuquerque (2009)

    Google Scholar 

  4. Diehl, P.: Implementierung eines Peridynamik-Verfahrens auf GPU. Diplomarbeit, Institute of Parallel and Distributed Systems, University of Stuttgart (2012)

    Google Scholar 

  5. Du, Q., Tian, X.: Robust discretization of nonlocal models related to peridynamics. In: Griebel, M., Schweitzer, M.A. (eds.) Meshfree Methods for Partial Differential Equations VII. Lecture Notes in Computational Science and Engineering, vol. 100, pp. 97–113. Springer, Heidelberg (2015)

    Google Scholar 

  6. Franzelin, F., Diehl, P., Pflüger, D.: Non-intrusive uncertainty quantification with sparse grids for multivariate peridynamic simulations. In: Griebel, M., Schweitzer, M.A. (eds.) Meshfree Methods for Partial Differential Equations VII. Lecture Notes in Computational Science and Engineering, vol. 100. Springer, Heidelberg (2014)

    Google Scholar 

  7. Ganzenmüller, G.C., Hiermaier, S., May, M.: Improvements to the Prototype Micro-Brittle Linaear Elasticity Model of Peridynamics. In: Griebel, M., Schweitzer, M.A. (eds.) Meshfree Methods for Partial Differential Equations VII. Lecture Notes in Computational Science and Engineering, vol. 100. Springer, Heidelberg (2014)

    Google Scholar 

  8. Leavy, R.B., Clayton, J.D., Strack, O.E., Brannon, R.M., Strassburger, E.: Edge on impact simulations and experiments. Proc. Eng. 58(0), 445–452 (2013). Proceedings of the 12th Hypervelocity Impact Symposium

    Google Scholar 

  9. Parks, M.L., Lehoucq, R.B., Plimpton, S.J., Silling, S.A.: Implementing peridynamics within a molecular dynamics code. Comput. Phys. Commun. 179, 777–783 (2008)

    Article  MATH  Google Scholar 

  10. Riedel, W., Hiermaier, S., Thoma, K.: Transient stress and failure analysis of impact experiments with ceramics. Mater. Sci. Eng. B 173, 139–147 (2010)

    Article  Google Scholar 

  11. Schradin, H.: Physikalische Vorgänge bei hohen Belastungen und Belastungsgeschwindigikeiten (Physical processes at high loadings and loading rates). In: Scripts for German Academy for Aeronautical Research, vol. 40, pp. 21–68 (1939)

    Google Scholar 

  12. Silling, S.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Silling, S.A.: A coarsening method for linear peridynamics. Int. J. Multiscale Comput. Eng. 9(6), 609–621 (2011)

    Article  Google Scholar 

  14. Silling, S., Askari, E.: A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83, 1526–1535 (2005)

    Article  Google Scholar 

  15. Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constititive modeling. J. Elast. 88, 151–184 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Strassburger, E.: Visualization of impact damage in ceramics using the edge-on impact technique. Int. J. Appl. Ceram. Technol. 1, 235–242 (2004)

    Article  Google Scholar 

  17. Strassburger, E., Patel, P., McCauley, J.W., Tempelton, D.W.: Visualization of wave propagation and impact damage in a polycrystalline transparent ceramic - AlON. In: 22nd International Symposium on Ballistics, vol. 2, pp. 769–776. DEStech Publications, Lancaster (2005)

    Google Scholar 

  18. Strassburger, E., Patel, P., McCauley, J.W., Templeton, D.W.: High-speed photographic study of wave propagation and iimpact damage in fused silcia and alon using the edge-on impact (EOI) method. AIP Conf. Proc. 892 (2006). doi:http://dx.doi.org/10.1063/1.2263465

  19. Winkler, S., Senf, H., Rothenhausler, H.: Wave and fracture phenomena in impacted ceramics. EMI-Report V5/89, Fraunhofer-Inst Fuer Werkstoffmechanik Freiburg (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Patrick Diehl .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Diehl, P., Schweitzer, M.A. (2015). Simulation of Wave Propagation and Impact Damage in Brittle Materials Using Peridynamics. In: Mehl, M., Bischoff, M., Schäfer, M. (eds) Recent Trends in Computational Engineering - CE2014. Lecture Notes in Computational Science and Engineering, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-22997-3_15

Download citation

Publish with us

Policies and ethics