A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects

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On penalization in variational phase-field models of brittle fracture (2018, background): “extended to ductile (elasto-plastic) fracture [27, 28, 29, 30, 31, 32, 33], fracture in films [34, 35], shells [36, 37, 38, 39], fracture under thermal loading [40, 41, 42], hydraulic fracture [43, 44, 45, 46, 47, 48], fracture in porous media [49, 50, 51], anisotropic fracture [52, 53, 54, 55, 56, ”
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, background): “The first group [59,62,107,108] uses the energy of the plastic deformation to sustain damage evolution, while the other [54,109,110] defines a critical strain and a penalty function to achieve fracture.”
Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow (2018, background): “[75]) becomes a function of the length parameter.”
A phase-field formulation for dynamic cohesive fracture (2018, background): “see Borden et al. (2012), which poses a significant limitation for many important crack propagation problems. In addition, such formulations typically exhibit nonlinear behavior immediately at the onset of loading. In the quest to develop a remedy to these issues, researchers have adopted a number o”