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 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 microstructural 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.
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e-mail: cvolokh@tx.technion.ac.il
e-mail: hjgao@mf.mpg.de
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November 2005
Technical Briefs
On the Modified Virtual Internal Bond Method
K. Y. Volokh,
e-mail: cvolokh@tx.technion.ac.il
K. Y. Volokh
Faculty of Civil and Environmental Engineering
, Technion, Haifa 32000, Israel
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H. Gao
e-mail: hjgao@mf.mpg.de
H. Gao
Max Planck Institute for Metals Research
, Heisenbergstrasse 3, Stuttgart 70569, Germany
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K. Y. Volokh
Faculty of Civil and Environmental Engineering
, Technion, Haifa 32000, Israele-mail: cvolokh@tx.technion.ac.il
H. Gao
Max Planck Institute for Metals Research
, Heisenbergstrasse 3, Stuttgart 70569, Germanye-mail: hjgao@mf.mpg.de
J. Appl. Mech. Nov 2005, 72(6): 969-971 (3 pages)
Published Online: April 5, 2005
Article history
Received:
November 2, 2004
Revised:
April 5, 2005
Citation
Volokh, K. Y., and Gao, H. (April 5, 2005). "On the Modified Virtual Internal Bond Method." ASME. J. Appl. Mech. November 2005; 72(6): 969–971. https://doi.org/10.1115/1.2047628
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