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Fracture modeling using meshless methods and level sets in 3D: framework and modeling. (English) Zbl 1352.74312
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.

MSC:
74R10 Brittle fracture
76S05 Flows in porous media; filtration; seepage
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S25 Spectral and related methods applied to problems in solid mechanics
Software:
XFEM; Gmsh; ToolboxLS
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References:
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