Phase-field modeling of hydraulic fracture

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A phase field formulation for hydrogen assisted cracking (2018, methodology): “The model builds upon Griffith’s thermodynamics framework and has not only been successfully applied to model brittle fracture but also to ductile damage [18,19], hydraulic fracturing [20,21], composites delamination [22,23], and stress corrosion cracking [24,25], to name a few.”
Crack nucleation in variational phase-field models of brittle fracture (2018, unknown): “They have been applied to a wide variety of fracture problems including fracture of ferro-magnetic and piezo-electric materials [1, 90], thermal and drying cracks [68, 22], or hydraulic fracturing [19, 89, 31, 91] to name a few.”
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, ”
A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics (2018, background): “The phase field models derived from microforce balance can be found in [46,47] for brittle materials, in [43] for capturing brittle–ductile transition of frictional-cohesive materials, Choo and Sun [44] for porous materials with growing crystal, and Na and Sun [38] for anisotropic fracture in crysta”