A time-discrete model for dynamic fracture based on crack regularization

By Blaise Bourdin, Christopher J. Larsen, Casey L. Richardson. 2011

328 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8a39cfe8ab52cd41d08ae39bf754eec29078cea6

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In Computational Theory and Mathematics

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Phase-field models for brittle and cohesive fracture (2014, unknown): “Applications to dynamic brittle fracture can be found in [4, 8, 15].”
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”
EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE (2010, unknown): “1”
Phase-field modeling of hydraulic fracture (2016, background): “Examples of diffuse crack approaches include peridynamics([37,38]), gradient damage mechanics([39,40]), and the phase-field methods presented herein and by other recent studies([41-53]).”
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].”
A phase-field formulation for dynamic cohesive fracture (2018, background): “d in Miehe et al. (2010a,b) and da Silva et al. (2013), which have broadened the scope of phase-eld modeling for fracture. With respect to dynamic fracture, phase-eld models have been considered in Bourdin et al. (2011), Borden et al. (2012), Hofacker and Miehe (2013), Schluter et al. (2014) and Li ”
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.”
Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, background): “A recent extension to dynamic fracture is outlined in Bourdin et al. (2001).”
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.”
Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials (2017, unknown): “Moreover, the phase field method has a low dependence to the mesh in a classical FEM framework and can handle very complex, multiple crack fronts, branching in both 2D and 3D without adhoc numerical treatment [8,21,28].”
Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy (2015, methodology): “Although it is not technically necessary from a mathematical standpoint [33], it is used to prevent ill-conditioning of stiffness matrix in the numerical implementation.”
A phase‐field model for cohesive fracture (2013, methodology): “Both models have been applied to dynamic fracture [23, 24, 25].”
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns (2013, background): “A recent extension to dynamic fracture is outlined in [20].”