Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds

Abstract A virtual internal bond (VIB) 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 that 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 VIB 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 VIB 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.