Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation

By M. Hofacker, C. Miehé. International Journal of Fracture, 2012

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Phase‐field modeling of ductile fracture at finite strains: A robust variational‐based numerical implementation of a gradient‐extended theory by micromorphic regularization (2017, background): “This diffusive crack modeling allows the resolution of complex failure topologies, such as crack branching phenomena in dynamic fracture of brittle solids, see Hofacker & Miehe [53] and the references cited therein.”
Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms (2017, methodology): “the most widely used model [11,44,29,8,15] is given by(1):”
Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation (2017, background): “directions as attested in papers on various solution techniques [39, 50, 53, 1, 3, 48, 27, 74, 24], isogeometric analysis [12, 11, 34, 4, 33], discontinuous/enriched Galerkin [23, 58], adaptive (spatial) discretizations [18, 19, 8, 72], dynamic fracture [40, 41, 12, 16, 35, 62], ductile/cohesive fra”
An efficient phase-field model for fatigue fracture in ductile materials (2019, unknown): “Miehe et al. [13] interpreted the phase-field variable in the sense of damage and therefore introduced the crack driving force as the maximum energy density in time history H = 2`Gc max s∈[0;t] ψe(ε, s), (6) ensuring local irreversibility for the phase-field.”