Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Abstract

SUMMARY In 3D fracture modeling, the complexity of the evolving crack geometry during propagation raises challenges in stress analysis because the accuracy of results mainly relies on the accurate description of the crack geometry. In this paper, a numerical framework is developed for 3D fracture modeling where a meshless method, the element‐free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution. In this framework, a simple and general formulation for associating the displacement jump in the field approximation with an arbitrary 3D curved crack surface is proposed. For accurate closure of the crack front, a tying procedure is extended to 3D from its original use in 2D in the previous paper by the authors. The benefits of level sets in improving the results accuracy and reducing the computational cost are explored, particularly in the model refinement and the confinement of the displacement jump. Issues arising in level sets updating are discussed and solutions proposed accordingly. The developed framework is validated with a number of 3D crack examples with reference solutions and shows strong potential for general 3D fracture modeling. Copyright © 2012 John Wiley & Sons, Ltd.

Phase-field modeling of fracture in linear thin shells

“…Most of above methods are based on discrete crack models that require explicitly (or sometimes implicitly [17]) tracking the crack path. Furthermore, many of the approaches are applied to simple geometries such as plates, or spherical and cylindrical geometries [18,19,12,20].…”

Numerical Analysis on the Optimization of Hydraulic Fracture Networks

“…The second kind is meshless methods. Different from traditional methods, meshless methods [21][22][23] are free from meshing and have the capability to deal with moving boundary conditions. Meshless methods are flexible and computationally efficient in simulating fracture propagation, but have not been in used in simulating the complex fracture network propagation in hydraulic fracturing.…”

A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

“…Recently, much effort has been directed towards the application of meshless methods to crack problems to overcome the difficulties in traditional numerical methods [9][10][11][12][13][14][15][16][17][18][19]. Despite clear general progress with these methods, there are still some technical issues in their application to fracture problems, for instance, it is often awkward and an expensive task to refine the nodal arrangement near the crack tip in order to increase the solution accuracy, since the stress results tend to be oscillatory near the crack tip.…”

“…However, introducing such an enriched basis in meshless approximations can lead to ill-conditioning of the global stiffness matrix, and special treatments [12,17] have to be used to alleviate this problem. Thirdly, many meshless methods employ the J-integral or contour integral scheme for the calculation of SIF, which is performed as a post-processing step applied to the stress results, such as in the formulations using the FEM described in [15][16][17][18][19] and partition of unity enriched boundary element method (PU-BEM) [21,22]. This is unlike the case with the isoparametric FEM or sub-region mixed variational principle based FEM where the SIF can be directly obtained as part of the solution [3][4][5].…”