A method for multiple crack growth in brittle materials without remeshing

By Elisa Budyn, Goangseup Zi, Nicolas Moës, Ted Belytschko. 2004

271 citations recorded by the source corpus.

A method for modelling the growth of multiple cracks in linear elastic media is presented. Both homogeneous and inhomogeneous materials are considered. The method uses the extended finite element method for arbitrary discontinuities and does not require remeshing as the cracks grow; the method also treats the junction of cracks. The crack geometries are arbitrary with respect to the mesh and are described by vector level sets. The overall response of the structure is obtained until complete failure. A stability analysis of competitive cracks tips is performed. The method is applied to bodies in plane strain or plane stress and to unit cells with 2–10 growing cracks (although the method does not limit the number of cracks). It is shown to be efficient and accurate for crack coalescence and percolation problems. Copyright © 2004 John Wiley & Sons, Ltd.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7d5e005db0115fafa974e23636b187d90d988fe4

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A multiscale projection method for macro/microcrack simulations (2007, background): “[13] and in microcrack/macrocrack strategies by Guidault et al.”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “[38] for multiple interacting cracks in two dimensions.”
Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings (2012, unknown): “[4] but this strategy will be most likely very cumbersome in three dimensions.”
A review of extended/generalized finite element methods for material modeling (2009, background): “Applications of XFEM and level sets to problems with multiple intersecting and branching cracks can be found in Budyn et al. [20], Zi et al. [121] and Loehnert and Belytschko [69].”
A robust preconditioning technique for the extended finite element method (2011, background): “polycrystals [15], multiple cracks [16], and geometric enrichment [6]).”
A study of the representation of cracks with level sets (2007, methodology): “Similar methods with scalar level set functions are used in References [26–28].”
Material point method with enriched shape function for crack problems (2017, unknown): “[7] modelled the growth of multiple cracks.”
An efficient augmented finite element method for arbitrary cracking and crack interaction in solids (2014, background): “Special data structures have been developed for tracking the crack surfaces and for proper merging of DoFs associated with different interacting cracks [11, 15, 28, 29].”
A peridynamics formulation for quasi-static fracture and contact in rock (2017, unknown): “5 (a) (Budyn et al., 2004).”