EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE

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Crack nucleation in variational phase-field models of brittle fracture (2018, unknown): “They have been expended to account for dynamic effects [65, 23, 16, 57], ductile behavior [2, 77, 3], cohesive effects [35, 34, 45], large deformations [4, 76, 15], or anisotropy [69], for instance.”
A phase-field description of dynamic brittle fracture (2012, methodology): “Recently, this model has been applied in a dynamic setting by Bourdin, Larsen, and Richardson (2011); Larsen, Ortner, and Süli (2010); and Larsen (2010), but application to structures of engineering interest has not been considered.”
A time-discrete model for dynamic fracture based on crack regularization (2011, background): “In fact, we also get (see Larsen et al. (2010)) that the total energy (including the energy dissipated in forming the crack, and subtracting the work of external forces) is constant in time, and that solutions to our discretetime model converge to solutions of this continuoustime model as the time s”
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework (2014, methodology): “It has also been extended successfully to dynamic problems by Borden et al. [6], Bourdin, Larsen, and Richardson [11], Hofacker and Miehe [22], Larsen [26], and Larsen, Ortner, and Süli [27].”