The extended finite element method for dynamic fractures

By Goangseup Zi, Hao Chen, Jingxiao Xu, Ted Belytschko. 2005

73 citations recorded by the source corpus.

A method for modelling arbitrary growth of dynamic cracks without remeshing is presented. The method is based on a local partition of unity. It is combined with level sets, so that the discontinuities can be represented entirely in terms of nodal data. This leads to a simple method with clean data structures that can easily be incorporated in general purpose software. Results for a mixed-mode dynamic fracture problem are given to demonstrate the method.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/790afde21abd342c202f02a627cf70348ec856e5

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

Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation (2008, background): “This level set representation of cracks was also found to be extremely convenient to handle crack growth [7–9] (without any remeshing).”
Dynamic crack propagation analysis of orthotropic media by the extended finite element method (2009, methodology): “…include the work by Belytschko and Chen (2004) who developed a singular enrichment finite element method for elastodynamic crack propagation, Zi et al. (2005) who presented a method for modelling arbitrary growth of dynamic cracks without remeshing, and Menouillard et al. (2006) who…”
Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment (2008, unknown): “E-mail addresses: bordas@civil.gla.ac.uk (S. Bordas), Timon.Rabczuk@canterbury.ac.nz (T. Rabczuk), g-zi@korea.ac.kr (G. Zi).”
An explicit dynamics extended finite element method. Part 2: Element-by-element stable-explicit/explicit dynamic scheme (2009, methodology): “Based on the Partition of Unity (see Babuška and Melenk [1]), the X-FEM was first applied to dynamic crack growth simulations by Belytschko and co-authors [3, 42].”
Extended meshfree methods without branch enrichment for cohesive cracks (2007, unknown): “[52], also.”
A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks (2007, background): “[22, 31, 32, 45, 47]) and to dynamic problems ([6, 46]) in two dimensions.”
A scaled boundary polygon formulation for elasto-plastic analyses (2014, methodology): “The extension of polygon elements for fracture analysis [6, 7] have also been recently pursued by enriching the basis functions as in the extended finite element method (XFEM) [8].”