A virtual internal bond approach to modeling crack nucleation and growth

Most existing theories of fracture are based on small deformation constitutive models. These approaches are in contrast to the fact that extraordinarily large nonlinear elastic deformations inevitably occur during brittle fracture. As the small-strain constitutive laws are extrapolated to arbitrarily large strains, the crack tip material is also being extrapolated to sustaining arbitrarily large stresses without undergoing fracture. This nonphysical feature of conventional fracture mechanics models is remedied by adopting a phenomenological fracture criterion based on a critical stress intensity factor or energy release rate. Though the existing approaches have proved successful in a wide range of applications, they may be inapplicable for or have proved incapable of explaining experimental observations in which nonlinear, hyperelastic material response is an essential feature of the phenomenon.; 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 response of the material via the Cauchy-Born rule, by equating the strain energy function on the continuum level to the potential energy stored in the cohesive bonds due to an imposed deformation. The approach could be viewed as an attempt to provide a more physical basis for the hyperelastic constitutive laws used in finite strain continuum mechanics. Direct simulation of crack growth without a presumed nucleation, growth, or branching criterion is demonstrated through numerical examples.