An overview of the modelling of fracture by gradient damage models

By Jean-Jacques Marigo, C. Maurini, K. Pham. Meccanica (Milano. Print), 2016

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Crack nucleation in variational phase-field models of brittle fracture (2018, background): “We briefly summarize the solution of the uniaxial tension of a homogeneous bar [83, 86], referring the reader to the recent review [73] for further details: As one increases the applied strain, the damage field remains 0 and the stress field constant until it reaches the elastic limit σe = √ GcE cw`”
An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation (2020, methodology): “Since the first introduction of the method, numerous open-source implementations were proposed [32,33,39,44].”
Phase-field modeling of anisotropic brittle fracture including several damage mechanisms (2018, unknown): “Let us ﬁrst consider a generalization of damage gradient models used to model the behavior of quasi-brittle materials [4, 44].”
Comparison of Phase-Field Models of Fracture Coupled with Plasticity (2018, background): “As the internal length ` tends to zero, the phase-field variable, which can be mechanically interpreted as a damage variable [15], localizes towards the fracture path and the global minima of the phase-field energy functional tend towards those of the energy functional of Griffith’s brittle fracture”