## An extended finite element method with discontinuous enrichment for applied mechanicsThe additional incorporation of near-tip functions allows for a natural application of the enriched approximation to fracture mechanics. The capability to accurately calculate stress intensity factors for a mesh which does not conform to the crack geometry is a distinct advantage of the method. In addition to two-dimensional linear elastic fracture, the extension of the method to the modeling of mixed-mode fracture in Mindlin-Reissner plates is examined. To this end, a domain form of the interaction integral is developed for the extraction of moment and shear force intensity factors. The application of discontinuous enrichment to model interfaces with nonlinear constitutive laws is also developed. In conjunction with a well developed iterative technique, several different constitutive laws are considered on the discontinuous interface, including frictional contact on the crack faces. The simulation of crack growth in this context is straightforward, as the enrichment functions alone model the crack geometry such that no remeshing is necessary. The simulated crack paths are shown to correlate well with experimental data, and consistent results are obtained with the method throughout. |

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### Contents

Overview of Partition of Unity Methods | 11 |

Modeling Arbitrary Discontinuities | 33 |

An Enriched Formulation for Plate Fracture | 78 |

Copyright | |

6 other sections not shown

### Common terms and phrases

additional aligned angle Applied Mechanics approximating space Babuska basis functions Belytschko bilinear form calculated chapter components consider constitutive law construction contour integrals Convergence results crack faces crack geometry crack growth crack length crack paths crack propagates crack tip degrees of freedom denoted developed discontinuous enrichment discretizations displacement field divergence theorem Dolbow domain form element subdomains enriched approximation enrichment functions Erdogan Figure finite element approximation finite element method force intensity factors formulation fracture mechanics function H(x Galerkin method interaction integral interface International Journal intersected linear elastic load mesh meshless methods Mindlin-Reissner plates MITC4 mixed-mode model crack model problem near-tip enrichment near-tip fields near-tip functions nodal shape functions nodes whose support nonlinear constitutive laws normal partition of unity plate fracture present remeshing search direction shear force intensity shear locking shown in Fig simulation stress intensity factors tangential tractions uniform mesh unilateral contact vector weak form weight functions Young's modulus