Fracture analysis of cellular materials: A strain gradient model

J. Y. Chen, Y. Huang*, M. Ortiz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

148 Scopus citations


A generalized continuum model is developed for cellular materials based on the equivalence of strain energy at the macro-and microscale. It is rather similar to the strain gradient theory, but has a well-defined characteristic length, namely, the cell size. The continuum model enables one to use powerful analytical methods to investigate fracture of cellular materials. The near-tip asymptotic fields and full-field solutions are obtained for cellular materials with hexagonal, triangular, or square lattice. Using the same strain-energy equivalence at the macro-and microscale, displacements and rotation of discrete cell walls are estimated from the continuum near-tip asymptotic fields. By postulating a maximum-tensile-stress failure criterion of cell walls, the fracture toughness of cellular materials is estimated to be proportional to the thickness h of cell walls and inversely proportional to √L, where L is the cell size. Moreover, the mixed-mode fracture toughness can be simply obtained from the fracture toughness in pure mode I and mode II, once the mode mixity is known. It is established that, with the same mass density, the hexagonal or triangular lattice in a cellular material can provide much higher fracture toughness than the square lattice.

Original languageEnglish (US)
Pages (from-to)789-828
Number of pages40
JournalJournal of the Mechanics and Physics of Solids
Issue number5
StatePublished - May 1998


  • Cellular materials
  • Fracture
  • Strain gradient

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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