TY - JOUR
T1 - Modeling quasi-static crack growth with the extended finite element method Part I
T2 - Computer implementation
AU - Sukumar, N.
AU - Prévost, J. H.
N1 - Funding Information:
The financial support to J.-H.P. from the National Science Foundation through contract NSF-9988788, Dr. Jorn Larsen-Basse Program Manager, is gratefully acknowledged. This work was accomplished in Spring 2001 when N.S. was visiting Princeton University; the hospitality extended to him by Professor David Srolovitz is appreciated. The comments and suggestions of the anonymous reviewers are also acknowledged.
PY - 2003/12
Y1 - 2003/12
N2 - 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.
AB - 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.
KW - Crack modeling
KW - Extended finite element
KW - Finite element programming
KW - Partition of unity
KW - Singularity
KW - Strong discontinuities
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U2 - 10.1016/j.ijsolstr.2003.08.002
DO - 10.1016/j.ijsolstr.2003.08.002
M3 - Article
AN - SCOPUS:0242539664
SN - 0020-7683
VL - 40
SP - 7513
EP - 7537
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 26
ER -