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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Note that we assume isotropic material behavior due to the fact that s depends on \(\vert \vert \xi \vert \vert\).
References
Benson, D.J.: Computational methods in lagrangian and eulerian hydrocodes. Comput. Methods Appl. Mech. Eng. 99(2–3), 235–394 (1992)
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
Brannon, R., Fossum, A., Strack, E.: Kayenta: Theory and User’s Guide. Tech. Rep. SAND2009-2282, Sandia National Laboratories, Albuquerque (2009)
Diehl, P.: Implementierung eines Peridynamik-Verfahrens auf GPU. Diplomarbeit, Institute of Parallel and Distributed Systems, University of Stuttgart (2012)
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)
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)
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)
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
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)
Riedel, W., Hiermaier, S., Thoma, K.: Transient stress and failure analysis of impact experiments with ceramics. Mater. Sci. Eng. B 173, 139–147 (2010)
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)
Silling, S.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000)
Silling, S.A.: A coarsening method for linear peridynamics. Int. J. Multiscale Comput. Eng. 9(6), 609–621 (2011)
Silling, S., Askari, E.: A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83, 1526–1535 (2005)
Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constititive modeling. J. Elast. 88, 151–184 (2007)
Strassburger, E.: Visualization of impact damage in ceramics using the edge-on impact technique. Int. J. Appl. Ceram. Technol. 1, 235–242 (2004)
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)
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
Winkler, S., Senf, H., Rothenhausler, H.: Wave and fracture phenomena in impacted ceramics. EMI-Report V5/89, Fraunhofer-Inst Fuer Werkstoffmechanik Freiburg (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-3-319-22997-3_15
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22996-6
Online ISBN: 978-3-319-22997-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)