Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation

• Published in: International journal of solids and structures Vol. 40; no. 26; pp. 7513 - 7537
• Main Authors: Sukumar, N., Prévost, J.-H.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.12.2003; Elsevier Science
• Subjects: Computational techniques; Crack modeling; Exact sciences and technology; Extended finite element; Finite element programming; Finite-element and galerkin methods; Fracture mechanics (crack, fatigue, damage...); Fracture mechanics, fatigue and cracks; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Partition of unity; Physics; Singularity; Solid mechanics; Strong discontinuities; Structural and continuum mechanics; Crack modeling; Extended finite element; Singularity; Partition of unity; Finite element programming; Strong discontinuities
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2003.08.002

The extended finite element method (X-FEM) is a numerical method for modeling strong (displacement) as well as weak (strain) discontinuities within a standard finite element framework. In the X-FEM, special functions are added to the finite element approximation using the framework of partition of unity. For crack modeling in isotropic linear elasticity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are used to account for the crack. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence quasi-static crack propagation simulations can be carried out without remeshing. In this paper, we discuss some of the key issues in the X-FEM and describe its implementation within a general-purpose finite element code. The finite element program Dynaflow™ is considered in this study and the implementation for modeling 2-d cracks in isotropic and bimaterial media is described. In particular, the array-allocation for enriched degrees of freedom, use of geometric-based queries for carrying out nodal enrichment and mesh partitioning, and the assembly procedure for the discrete equations are presented. We place particular emphasis on the design of a computer code to enable the modeling of discontinuous phenomena within a finite element framework.