Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

By Ted Belytschko, Hao Chen, Jingxiao Xu, Goangseup Zi. 2003

600 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/7d482342ef34c6933cc05c65a7b80e97c9c961fb

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Dual‐horizon peridynamics (2015, methodology): “The crack propagation angle of two other methods [43, 46] are 65.”
Studies of dynamic crack propagation and crack branching with peridynamics (2010, methodology): “We decided to perform the peridynamic simulations using a setup similar to that used in a few recent simulation papers (Belytschko et al. 2003; Rabczuk and Belytschko 2004; Song et al. 2006).”
The extended finite element method for fracture in composite materials (2009, background): “We might add that XFEM has a wide variety of applications, such as dynamic crack propagation [13, 14], dislocations [15, 16] and large strain fracture mechanics [17].”
Cracking particles: a simplified meshfree method for arbitrary evolving cracks (2004, methodology): “However, these methods require an explicit representation of the crack surface, which has been provided by level sets in References [11, 12].”
An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation (2020, background): “Generally, branching was identified as an instability and the loss of hyperbolicity [19,20] of the acoustic matrix.”
New finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids (2011, neutral): “[12], among others.”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “Other interesting developments for cohesive cracks can be found in [112, 11, 5].”
A three dimensional large deformation meshfree method for arbitrary evolving cracks (2007, background): “[4]), an explicit representation of the crack surface is needed.”
Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, methodology): “Advanced extended finite element methods with nodal enrichment for dynamic fracture are outlined e.g. in Belytschko et al. (2003), Song and Belytschko (2009), Song et al. (2008, 1984), and Fagerström and Larsson (2006).”
A computational library for multiscale modeling of material failure (2013, background): “The loss of hyperbolicity criterion is another criterion for crack nucleation and propagation [18] which is used in PER-MIX.”
A phase-field formulation for dynamic cohesive fracture (2018, methodology): “Following Belytschko et al. (2003), we therefore consider a velocity boundary condition applied to the notched area with magnitude v0 = 16.5 m/s, linearly ramped up from zero over a time interval of tR = 1 μs. The maraging steel used in the original experiments is modeled using the following materia”
A phase-field description of dynamic brittle fracture (2012, methodology): “Previous numerical results of this problem based on XFEM have been reported by Belytschko et al. (2003), among others, and a comparison of results between XFEM, the element deletion method, and the interelement crack method have been reported by Song, Wang, and Belytschko (2008). Numerical results o”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “Therefore, a modified step enrichment is proposed in [24] which allows for inner-element crack tips.”
A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM (2006, background): “• Nodal enrichment [4] [5] [16] [17] [33] [35]: the support of each mode is the one of a given nodal shape function i.e.: those elements surrounding a specific node, see Fig.”
GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004, methodology): “([28, 23]) and certain non-linear problems ([ 8 ]).”