Evolving crack patterns in thin films with the extended finite element method

J. Liang, R. Huang, J. H. Prévost, Z. Suo

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


This paper develops the extended finite element method (XFEM) to evolve patterns of multiple cracks, in a brittle thin film bonded to an elastic substrate, with a relatively coarse mesh, and without remeshing during evolution. A shear lag model describes the deformation in three dimensions with approximate field equations in two-dimensions. The film is susceptible to subcritical cracking, obeying a kinetic law that relates the velocity of each crack to its energy release rate. At a given time, the XFEM solves the field equations and calculates the energy release rate of every crack. For a small time step, each crack is extended in the direction of maximal hoop stress, and by a length set by the kinetic law. To confirm the accuracy of the XFEM, we compare our simulation to the exiting solutions for several simple crack patterns, such as a single crack and a set of parallel cracks. We then simulate the evolution of multiple cracks, initially in a small region of the film but of different lengths, showing curved crack propagation and crack tip shielding. Starting with multiple small cracks throughout the film, the XFEM can generate the well-known mud crack pattern.

Original languageEnglish (US)
Pages (from-to)2343-2354
Number of pages12
JournalInternational Journal of Solids and Structures
Issue number10
StatePublished - Jun 2003

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Crack patterns
  • Extended finite element method
  • Subcritical cracking
  • Thin films


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