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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002407
pages 675-688


John T. Foster
Mechanical Engineering Department, University of Texas, San Antonio, TX 78249, USA; Terminal Ballistics Technology, Sandia National Laboratories, Albuquerque, New Mexico 87185,USA
Stewart A. Silling
Multiscale Dynamic Material Modeling Department, Sandia National Laboratories, Albuquerque, New Mexico,87185, USA
Weinong Chen
Aeronautics and Astronautics and Materials Engineering, Purdue University, West Lafayette, Indiana 47907, USA


Peridynamics is a continuum reformulation of the standard theory of solid mechanics. Unlike the partial differential equations of the standard theory, the basic equations of peridynamics are applicable even when cracks and other singularities appear in the deformation field. Interactions between continuum material points are termed "bonds." In this paper, a method for implementing a rate-dependent plastic material model within a peridynamic numerical code is summarized and a novel failure criterion is then presented by analyzing the energy required to break all bonds across a plane of unit area (energy release rate); with this, one can determine the critical energy density required to irreversibly fail a single bond. By failing individual bonds, this allows cracks to initiate, coalesce, and propagate without a prescribed external crack law. This is demonstrated using experimentally collected fracture toughness measurements to evaluate the energy release rate. Simulations are compared to experimental results.


  1. Askari, E., Bobaru, F., Lehoucq, R., Parks, M., Silling, S., and Weckner, O., Peridynamics for multiscale materials modeling. DOI: 10.1088/1742-6596/125/1/012078

  2. Foster, J., Dynamic crack initiation toughness: Experiments and peridynamic modeling. DOI: 10.2172/1001000

  3. Foster, J., Silling, S., and Chen, W., Viscoplasticity using peridynamics. DOI: 10.1002/nme.2725

  4. Foster, J., Chen, W., and Luk, V., Dynamic crack initiation toughness of 4340 steel at constant loading rates. DOI: 10.1016/j.engfracmech.2011.02.019

  5. Frew, D., Forrestal,M., and Chen,W., Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar. DOI: 10.1177/0014485105052111

  6. Rosakis, A., Duffy, J., and Freund, L., The determination of dynamic fracture toughness of AISI 4340 steel by the Shadow Spot Method. DOI: 10.1016/0022-5096(84)90030-9

  7. Silling, S., Reformulation of elasticity theory for discontinuities and long-range forces. DOI: 10.1016/S0022-5096(99)00029-0

  8. Silling, S., Dynamic fracture modeling with a meshfree peridynamic code. DOI: 10.1016/B978-008044046-0/50157-3

  9. Silling, S. and Askari, E., A meshfree method based on the peridynamic model of solid mechanics. DOI: 10.1016/j.compstruc.2004.11.026

  10. Silling, S. and Lehoucq, R., Convergence of peridynamics to classical elasticity theory. DOI: 10.1007/s10659-008-9163-3

  11. Silling, S., Epton, M., Weckner, O., Xu, J., and Askari, E., Peridynamic states and constitutive modeling. DOI: 10.1007/s10659-007-9125-1

  12. Silling, S., Zimmermann, M., and Abeyaratne, R., Deformation of a peridynamic bar. DOI: 10.1023/B:ELAS.0000029931.03844.4f

  13. Warren, T. and Tabbara, M., Simulations of the penetration of 6061-T6511 aluminum targets by spherical-nosed VAR 4340 steel projectiles. DOI: 10.1016/S0020-7683(99)00148-1