Crack nucleation and growth as strain localization in a virtual-bond continuum

Abstract 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 VIB model to failure detection, dynamic crack propagation, and fracture toughening with combined fracture and constrained plasticity in a multilayered structure.

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