A phase-field description of dynamic brittle fracture
Citations
880 citations
Cites background or methods from "A phase-field description of dynami..."
...The early quasi-static formulations have been extended to the dynamic case in [20–25]....
[...]
...[22], 2012, Hofacker and Miehe [23,24], 2012, 2013, Schlüter et al....
[...]
...[10,15,16] and [22], enabling to test the phasefield method in general, as well as the performance of the various particular formulations....
[...]
...in [22], the difference between decompositions Eqs....
[...]
...The pre-existing crack is modeled by defining an initial strainhistory field as in [22]....
[...]
721 citations
Cites background from "A phase-field description of dynami..."
...The initial strain history function (H(x, 0)) could be defined as a function of the closest distance from x to the line (l), which represents the discrete crack [35]....
[...]
522 citations
Cites background from "A phase-field description of dynami..."
...Phase-field modeling of brittle fracture [1-4] is a well-established framework that overcomes the limitations of the classical Griffith theory in the prediction of crack nucleation and in the identification of complicated crack paths including branching and merging....
[...]
522 citations
Cites methods from "A phase-field description of dynami..."
..., [18, 83], and the thick level set method [85]....
[...]
...A phase field model for dynamic fracture was presented in [18] using adaptive T-spline refinement to provide an effective method for simulating fracture in three dimensions....
[...]
435 citations
References
5,815 citations
"A phase-field description of dynami..." refers background in this paper
...• They obey the convex hull property, see Piegl and Tiller (1997). • Local refinement is possible. For additional details on basic T-spline analysis technology see Scott et al. (2010). The spline-based analysis strategy of isogeometric analysis has shown some advantages when compared to standard C finite elements. First, isogeometric analysis allows for the efficient and exact geometric representation of many objects of engineering interest. Also, when using T-spline-based isogeometric analysis, efficient and automatic local mesh refinement strategies exist that preserve the exact geometry. Secondly, the isogeometric basis is in general smooth. Although the phase-field model permits the use of traditional C finite elements, the use of a smooth base is anticipated to have favorable effects. One is that stresses are represented more accurately than with traditional C finite elements, which has been observed to yield efficient spatial discretizations for discrete (see Verhoosel et al. (2010)) and smeared (see Verhoosel et al. (2011)) fracture models....
[...]
...• They obey the convex hull property, see Piegl and Tiller (1997). • Local refinement is possible. For additional details on basic T-spline analysis technology see Scott et al. (2010). The spline-based analysis strategy of isogeometric analysis has shown some advantages when compared to standard C finite elements....
[...]
...• They obey the convex hull property, see Piegl and Tiller (1997). • Local refinement is possible. For additional details on basic T-spline analysis technology see Scott et al. (2010). The spline-based analysis strategy of isogeometric analysis has shown some advantages when compared to standard C finite elements. First, isogeometric analysis allows for the efficient and exact geometric representation of many objects of engineering interest. Also, when using T-spline-based isogeometric analysis, efficient and automatic local mesh refinement strategies exist that preserve the exact geometry. Secondly, the isogeometric basis is in general smooth. Although the phase-field model permits the use of traditional C finite elements, the use of a smooth base is anticipated to have favorable effects. One is that stresses are represented more accurately than with traditional C finite elements, which has been observed to yield efficient spatial discretizations for discrete (see Verhoosel et al. (2010)) and smeared (see Verhoosel et al....
[...]
...• They obey the convex hull property, see Piegl and Tiller (1997). • Local refinement is possible....
[...]
5,516 citations
"A phase-field description of dynami..." refers methods in this paper
...The variational formulation for quasi-static brittle fracture leads to an energy functional that closely resembles the potential presented by Mumford and Shah (1989), which is encountered in image segmentation....
[...]
5,137 citations
"A phase-field description of dynami..." refers methods in this paper
...In contrast to earlier work on phase-field models, we have chosen to use isogeometric spatial discretizations as introduced by Hughes et al. (2005), which are based on NURBS and T-splines....
[...]
4,897 citations
[...]
4,552 citations