A mechanism-based gradient damage model for metallic fracture

A small deformations effective stress model of gradient plasticity phase-field fracture

“…To account for the propagation of fracture driven by the development of localized plasticity, the functional L n p in ( 16) is enriched by the addition of the energy dissipated by the damage-like phase field d, responsible for the material stiffness and strength degradation. Since in the presence of softening structural response plastic strains tend to localize in a zero-thickness band, a further regularization of the model becomes necessary (see, e.g., [10,19,12,13,20]). A common and effective provision, motivated by microscale considerations (see, e.g., [39,40]) consists in introducing into the model a diffusive term of an inelastic, irreversible quantity (see, e.g., [41,42]).…”

“…where the free energy ψ 0 is defined in (2) and the increment of plastic dissipation ∆ϕ p 0 in (12). Defining…”

“…Several authors have proposed extensions of the phase-field formulation of brittle fracture incorporating plastic dissipation mechanisms. In the small deformation framework, local plasticity has been addressed, e.g., in [3,4,5,4,6,7,8,9], while gradient plasticity mechanisms have been considered in [10,11,12,13]. In the large deformation framework, the models [14,15,16,17,18] deal with local plasticity, while gradient plasticity has been included in the formulation in [19,20,21].…”

A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface

“…Phase field fracture methods have become the de facto choice for modelling a wide range of cracking phenomena. New phase field formulations have been presented for ductile fracture [5,6], composite materials [7][8][9], shape memory alloys [10,11], functionally graded materials [12,13], fatigue damage [14,15] and hydrogen embrittlement [16,17], among others (see Refs. [18,19] for an overview).…”

A stress-based poro-damage phase field model for hydrofracturing of creeping glaciers and ice shelves

“…Phase field fracture models have gained remarkable popularity in recent years due to their ability to predict complex cracking phenomena including crack bifurcation, coalescence and nucleation from arbitrary sites [23][24][25]. New phase field-based formulations have been presented for dynamic fracture [26,27], ductile damage [28,29], environmentally assisted cracking [30,31], fatigue crack growth [32,33], hydraulic fracture [34,35], and battery degradation [36,37]; among other (see Refs. [38,39] for an overview).…”