Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update

By Anthony Gravouil, Nicolas Moës, Ted Belytschko. 2002

625 citations recorded by the source corpus.

We present a level set method for treating the growth of non‐planar three‐dimensional cracks.The crack is defined by two almost‐orthogonal level sets (signed distance functions). One of them describes the crack as a two‐dimensional surface in a three‐dimensional space, and the second is used to describe the one‐dimensional crack front, which is the intersection of the two level sets. A Hamilton–Jacobi equation is used to update the level sets. A velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface. The technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity. This displacement field is constructed directly in terms of the level sets, so the discretization by finite elements requires no explicit representation of the crack surface. Numerical experiments show the robustness of the method, both in accuracy and in treating cracks with significant changes in topology. Copyright © 2002 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f318e48ff0910405c87885450c37a999e00adbf1

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Improved implementation and robustness study of the X‐FEM for stress analysis around cracks (2005, positive): “The level-set update scheme is not described here; it is similar to the previously published paper [17], with some enhancements in the propagation stage (after velocity extension and before reinitialization and re-orthogonalization).”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “Belytschko and co-workers coupled the XFEM with level set method for static crack and crack growth simulations [ 26 ,39,71].”
Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, methodology): “x/, are used to describe the crack surface [3] in 3D.”
Enriched finite elements and level sets for damage tolerance assessment of complex structures (2006, methodology): “The presentation in this section follows closely [12,13] to which the interested reader is referred for more details.”
Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation (2008, background): “At about the same time, two level sets were introduced to conveniently store the crack as two finite element fields [6, 7].”
Dual‐horizon peridynamics (2015, background): “Also, the extension of peridynamics from 2D to 3D problems is greatly facilitated, which is not always the case in other methods [22, 23].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “On knowing the magnitude and orientation of crack growth, both φ n and φ t are updated using the level set method (Gravouil et al. 2002).”
A study of the representation of cracks with level sets (2007, methodology): “Again, a difference in this presentation with respect to Reference [5] is that we use a unit time step.”
An interaction integral method for 3D curved cracks in nonhomogeneous materials with complex interfaces (2010, methodology): “Moës et al. (2002) and Gravouil et al. (2002) used the method combined with the XFEM to study non-planar 3D crack growth problems.”