Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials

Zhengyu Jenny Zhang, Glaucio H. Paulino, Waldemar Celes

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136 Scopus citations


Dynamic crack microbranching processes in brittle materials are investigated by means of a computational fracture mechanics approach using the finite element method with special interface elements and a topological data structure representation. Experiments indicate presence of a limiting crack speed for dynamic crack in brittle materials as well as increasing fracture resistance with crack speed. These phenomena are numerically investigated by means of a cohesive zone model (CZM) to characterize the fracture process. A critical evaluation of intrinsic versus extrinsic CZMs is briefly presented, which highlights the necessity of adopting an extrinsic approach in the current analysis. A novel topology-based data structure is employed to enable fast and robust manipulation of evolving mesh information when extrinsic cohesive elements are inserted adaptively. Compared to intrinsic CZMs, which include an initial hardening segment in the traction-separation curve, extrinsic CZMs involve additional issues both in implementing the procedure and in interpreting simulation results. These include time discontinuity in stress history, fracture pattern dependence on time step control, and numerical energy balance. These issues are investigated in detail through a 'quasi-steady-state' crack propagation problem in polymethylmethacrylate. The simulation results compare reasonably well with experimental observations both globally and locally, and demonstrate certain advantageous features of the extrinsic CZM with respect to the intrinsic CZM.

Original languageEnglish (US)
Pages (from-to)893-923
Number of pages31
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
StatePublished - Nov 19 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Branching
  • Cohesive zone model (CZM)
  • Dynamic fracture
  • Extrinsic
  • Finite element method
  • Instability
  • Intrinsic
  • Topological data structure


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