Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds
H. Gao and P. Klein
Journal of the Mechanics and Physics of Solids, 46, 187-218 (1998).

ABSTRACT
A virtual internal bond (VIE) model with randomized cohesive interactions
between material particles is proposed as an integration of continuum models
with cohesive surfaces and atomistic models with interatomic bonding. This
approach differs from an atomistic model in thai a phenomenological "cohesive
force law" is assumed to act between "material particles" which are not
necessarily atoms; it also differs from a cohesive surface model in that,
rather than imposing a cohesive law along a prescribed set of discrete
surfaces, a randomized 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 function on the continuum level to the potential
energy stored in the cohesive bonds due to an imposed deformation. This work
is motivated by the notion that materials exhibit multiscale cohesive behaviors
ranging from interatomic bonding to macroscopic ductile failure. It is shown
that the linear elastic behavior of the VIE model is isotropic and obeys the
Cauchy relation; the instantaneous elastic properties under equibiaxial
stretching are transversely isotropic, with all the in-plane components of
the material tangent moduli vanishing at the cohesive stress limit; the
instantaneous properties under equitriaxial stretching are isotropic with
a finite strain modulus. We demonstrate through two preliminary numerical
examples that the VIE model can be applied in direct simulation of crack
growth without a presumed fracture criterion. The prospect of this type of
approach in numerical simulations of fracture seems to be highly promising.