Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation |
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Authors: | N Sukumar J -H Prvost |
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Institution: | 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 |
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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 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. |
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Keywords: | Strong discontinuities Partition of unity Extended finite element Finite element programming Crack modeling Singularity |
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