Peridynamic formulation of the mean stress and incubation time fracture criteria and its correspondence to the classical Griffith’s approach

Abstract

Peridynamic formulations of the mean stress and incubation time fracture models are discussed in the paper. Contemporary fracture simulations using the peridynamic theory often rely on critical bond stretch fracture criterion which is known to operate similarly to energybased fracture models. The energy-based fracture criteria -both in classical Griffith's and Irwin's form -are known to be powerful tools for fracture simulations and analysis. However, a number of experimentally observed dynamic fracture effects cannot be captured by these models, e.g. rate sensitivity of the material toughness. Thus, coupling of peridynamic approach with alternative stress-based fracture models would possibly broaden the peridynamics applicability. Here implementation technique of the aforementioned fracture model is discussed and its results for the case of a dynamically propagating crack with relatively low velocity due to quasistatic load appear to be in good agreement with the classical energy release rate approach.

Indentation fracture resistance of brittle materials using irregular cracks: A review

“…In this method, models and simulations explain the role Van der Waals forces play in the prediction of cracks behavior of brittle materials [ [96] , [97] , [98] , [99] ]. The combination of the two methods, peridynamics theory and VIF [ 100 , 101 ], based on Griffith theory could be a new approach and a vast evolution in determining K IFR / K IC for various materials, composites, and biological hard tissues.…”