Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation N. Sukumar a, * , J.-H. Pr evost b a Department of Civil and Environmental Engineering, University of California, One Shields Avenue, Davis, CA 95616, USA b Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA Received 30 October 2002; received in revised form 30 May 2003 Abstract 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 ac- count 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 Dynaflowe 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 free- dom, 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. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Strong discontinuities; Partition of unity; Extended finite element; Finite element programming; Crack modeling; Singularity 1. Introduction A problem of significant interest and importance in solid mechanics is the modeling of fracture and damage phenomena. These material failure processes manifest themselves in quasi-brittle materials such as rocks and concrete as fracture process zones, shear (localization) bands in ductile metals, or discrete crack discontinuities in brittle materials. The accurate modeling and the evolution of smeared and discrete * Corresponding author. Tel.: +1-530-7546415; fax: +1-530-7527872. E-mail address: [email protected] (N. Sukumar). 0020-7683/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2003.08.002 International Journal of Solids and Structures 40 (2003) 7513–7537 www.elsevier.com/locate/ijsolstr
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation
May 19, 2023
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