Dynamic Fracture Analysis with State-based Peridynamic Model: Crack Patterns on Stress Waves for Plane Stress Elastic Solid

상태 기반 페리다이나믹 모델에 의한 동적취성파괴 해석: 평면응력 탄성체의 응력 전파와 균열패턴 분석

Ha, Youn Doh

  • Received : 2015.04.07
  • Accepted : 2015.04.14
  • Published : 2015.06.30


A state-based peridynamic model is able to describe a general constitutive model from the standard continuum theory. The response of a material at a point is dependent on the deformation of all bonds connected to the point within the nonlocal horizon region. Therefore, the state-based peridynamic model permits both the volume and shear changes of the material which is promising to reproduce the complicated dynamic brittle fracture phenomena, such as crack branching, secondary cracks, cascade cracks, crack coalescence, etc. In this paper, the two-dimensional state-based peridynamic model for a linear elastic plane stress solid is employed. The damage model incorporates the energy release rate and the peridynamic energy potential. For brittle glass materials, the impact of the crack-parallel compressive stress waves on the crack branching pattern is investigated. The peridynamic solution for this problem captures the main features, observed experimentally, of dynamic crack propagation and branching. Cascade cracks under strong tensile loading and secondary cracks are also well reproduced with the state-based peridynamic simulations.


State-based peridynamic model;dynamic fracture;crack branching;stress waves


  1. Bobaru, F., Ha, Y.D., Hu, W. (2012) Damage Progression from Impact in Multilayered Glass Modeled with Peridynamics, Central European J. Eng., 2(4), pp.551-561.
  2. Bowden, F.P., Brunton, J.H., Field, J.E., Heyes, A.D. (1967) Controlled Fracture of Brittle Solids and Interruption of Electrical Current, Nature, 216, pp.38-42.
  3. Doll, W. (1975) Investigations of the Crack Branching Energy, Int. J. Fract., 11, pp.184-186.
  4. Ha, Y.D., Bobaru, F. (2010) Studies of Dynamic Crack Propagation and Crack Branching with Peridynamics, Int. J. Fract., 162(1-2), pp.229-244.
  5. Ha, Y.D., Bobaru, F. (2011) Characteristics of Dynamic Brittle Fracture Captured with Peridynamics, Eng. Fract. Mech., 78(6), pp.1156-1168.
  6. Ha, Y.D., Cho, S. (2011) Dynamic Brittle Fracture Captured with Peridynamics: Crack Branching Angle & Crack Propagation Speed, J. Comput. Struct. Eng. Inst. Korea, 24(6), pp.637-643.
  7. Ha, Y.D., Cho, S. (2012) Nonlocal Peridynamic Models for Dynamic Brittle Fracture in Fiber- Reinforced Composites: Study on Asymmetrically Loading State, J. Comput. Struct. Eng. Inst. Korea, 25(4), pp. 279-292.
  8. Ha, Y.D., Lee, J., Hong, J-W. (2014) Fracturing Patterns of Rock-like Materials in Compression Captured with Peridynamics, Eng. Fract. Mech., Submitted.
  9. Ha, Y.D. (2015) State-based Peridynamic Modeling for Dynamic Fracture of Plane Stress, J. Comput. Struct. Eng. Inst.Korea, accepted.
  10. Hu, W., Ha, Y.D., Bobaru, F. (2011) Modeling Dynamic Fracture and Damage in Fiber-Reinforced Composites with Peridynamics, Int. J. Multiscale Comput. Eng., 9(6), pp.707-726.
  11. Hu, W., Ha, Y.D., Bobaru, F. (2012) Peridynamic Model for Dynamic Fracture in Unidirectional Fiber-Reinforced Composites, Comput. Methods Appl. Mech.& Eng., 217, pp.247-261.
  12. Le, Q.V., Chan, W.K., Schwartz, J. (2014) A Two-Dimensional Ordinary, State-based Peridynamic Model for Linarly Elastic Solids, Int. J. Numer. Methods Eng., 98, pp.547-561.
  13. Ravi-Chandar, K., Knauss, W.G. (1944) An Experimental Investigation into Dynamic Fracture: IV. On the Interaction of Stress Waves with Propagating Cracks, Int. J. Fract., 26, pp.189-200.
  14. Silling, S.A. (2000) Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces, J. Mech.& Phys. Solids, 48, pp.175-209.

Cited by

  1. Peridynamic Modeling for Crack Propagation Analysis of Materials vol.31, pp.2, 2018,


Supported by : 한국연구재단