An extended finite element method for modeling crack growth with frictional contact

By John Dolbow, Nicolas Moës, Ted Belytschko. 2001

607 citations recorded by the source corpus.

Abstract A new technique for the finite element modeling of crack growth with frictional contact on the crack faces is presented. The eXtended Finite Element Method (X-FEM) is used to discretize the equations, allowing for the modeling of cracks whose geometry are independent of the finite element mesh. This method greatly facilitates the simulation of a growing crack, as no remeshing of the domain is required. The conditions which describe frictional contact are formulated as a non-smooth constitutive law on the interface formed by the crack faces, and the iterative scheme implemented in the LATIN method [Nonlinear Computational Structural Mechanics, Springer, New York, 1998] is applied to resolve the nonlinear boundary value problem. The essential features of the iterative strategy and the X-FEM are reviewed, and the modifications necessary to integrate the constitutive law on the interface are presented. Several benchmark problems are solved to illustrate the robustness of the method and to examine convergence. The method is then applied to simulate crack growth when there is frictional contact on the crack faces, and the results are compared to both analytical and experimental results.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/de299298aebf10d3a30e33ade44fe131679299a1

How researchers see this paper

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

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test (2004, background): “[15] demonstrated how to enforce nonlinear dissipative constitutive laws on the discontinuity surface.”
Imposing Dirichlet boundary conditions in the extended finite element method (2006, background): “[22] for the treatment of frictional contact on an interface with an enriched basis and was again studied in Reference [16].”
An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies (2013, methodology): “It was then adopted in modeling holes and inclusions [12], arbitrary discontinuities in solid materials [13], crack growth with frictional contact [14], cohesive crack propagation [15,16], and curved cracks [17].”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “The X-FEM has been successfully applied to 2-dimensional static and quasi-static crack growth problems (Mo€es et al., 1999; Dolbow, 1999; Dolbow et al., 2000a,b; Dolbow et al., 2001; Mo€es and Belytschko, 2002), with its extension to modeling holes, and branched and intersecting cracks proposed in D”
Numerical Methods for Fluid-Structure Interaction — A Review (2012, methodology): “…method (Udaykumar et al. 1996, 1999, 2001; Ye et al. 1999), the blob projection method (Cortez and Minion 2000), the extended finite element method (Dolbow et al. 2001, Moës et al. 1999), the lattice Boltzmann method (Lallemand and Luo 2003, Owen et al. 2010), the meshfree method (Belytschko et…”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “Practical applications are found for example in crack propagation with frictional contact [59, 105],”
A PGD-based homogenization technique for the resolution of nonlinear multiscale problems (2013, methodology): “Some extensions of the LATIN method coupled with the XFEM approach can be found in [38,39].”
High‐order extended finite element method for cracked domains (2005, methodology): “Several recent works have shown the efficiency of this method for two or three dimensional fracture problems [9, 25, 6, 11, 24, 15, 17, 20, 7].”
A high‐order generalized FEM for through‐the‐thickness branched cracks (2007, positive): “Further, cohesive or frictional contact laws [21, 40–52] can be incorporated by appropriate modifications of the formulation reported in [6, Sec.”
Dynamic crack propagation analysis of orthotropic media by the extended finite element method (2009, methodology): “Further general improvements have been made by Sukumar et al. (2000), Dolbow et al. (2001), Belytschko et al. (2003), Belytschko and Chen (2004), Asadpoure et al. (2006a,b), and Asadpoure and Mohammadi (2007), while specific extensions in field of dynamic crack propagation have recently been made…”
Stress analysis around crack tips in finite strain problems using the eXtended finite element method (2005, methodology): “Several fracture mechanics applications have been solved with the X-FEM approach: crack growth with friction [6], arbitrary branched and intersecting cracks [7], three dimensional crack propagation [8, 9] and cohesive crack simulation [10, 11].”