Crack nucleation and growth as strain localization in a virtual-bond continuum
P. Klein and H. Gao
Engineering Fracture Mechanics, 61, 21–48 (1998).


We have recently proposed a virtual internal bond (VIB) model with cohesive
interactions between material particles as an alternative approach to modeling
fracture. This approach differs from atomistic methods in that a
phenomenological "cohesive force law" is assumed to act between "material
particles" which are not necessarily atoms; it also differs from "cohesive
surface" models in that, rather than imposing a cohesive law along a
prescribed set of discrete surfaces, a network of cohesive bonds is
statistically incorporated into the constitutive law of the material via
the Cauchy-Born rule, i.e. by equating the strain energy density on the
continuum level to the potential energy stored in the cohesive bonds due to
an imposed deformation. With this approach, crack initiation and growth occur
spontaneously when the classical condition for the loss of ellipticity in the
elastic governing equations is satisfied. We demonstrate the application of
the VIE model to failure detection, dynamic crack propagation, and fracture
toughening with combined fracture and constrained plasticity in a multilayered