On the modified virtual internal bond method

K. Y. Volokh, H. Gao

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


The virtual internal bond (VIB) method was developed for the numerical simulation of fracture processes. In contrast to the traditional approach of fracture mechanics where stress analysis is separated from a description of the actual process of material failure, the VIB method naturally allows for crack nucleation, branching, kinking, and arrest. The idea of the method is to use atomic-like bond potentials in combination with the Cauchy-Born rule for establishing continuum constitutive equations which allow for the material separation-strain localization. While the conventional VIB formulation stimulated successful computational studies with applications to structural and biological materials, it suffers from the following theoretical inconsistency. When the constitutive relations of the VIB model are linearized for an Isotropic homogeneous material, the Poisson ratio is found equal to 1/4 so that there is only one independent elastic constant - Young's modulus. Such restriction is not suitable for many materials. In this paper, we propose a modified VIB (MVIB) formulation, which allows for two independent linear elastic constants. It is also argued that the discrepancy of the conventional formulation is a result of using only two-body interaction potentials in the micro-structural setting of the VIB method. When many-body interactions in "bond bending" are accounted for, as in the MVIB approach, the resulting formulation becomes consistent with the classical theory of isotropic linear elasticity.

Original languageEnglish
Pages (from-to)969-971
Number of pages3
JournalJournal of Applied Mechanics, Transactions ASME
Issue number6
StatePublished - 1 Nov 2005
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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