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

By Xiaoying Zhuang, Charles E. Augarde, K. Mathisen. 2012

339 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/800c6c8a085de57ad927344a1314746896b1a0ba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy (2017, methodology): “Models developed with this approach include, but are not limited to, cohesive interface elements with or without remeshing [15-22], elements with embedded strong discontinuities [23-28], extended finite elements methods [29-34], and meshless and particle methods [35-39].”
Stability analysis of slopes using the vector sum numerical manifold method (2020, methodology): “To avoid the drawbacks of the LEMs, many numerical methods (Zienkiewicz and Taylor 2000; Zhuang et al. 2012; Rabczuk et al. 2010; Yang et al. 2017, 2018a, c; Yang and Zheng 2016, 2017; Xu et al. 2020; Wu et al. 2020) have been proposed.”