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Modeling of dynamic crack branching by enhanced extended finite element method

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Abstract

The conventional extended finite element method (XFEM) is enhanced in this paper to simulate dynamic crack branching, which is a top challenge issue in fracture mechanics and finite element method. XFEM uses the enriched shape functions with special characteristics to represent the discontinuity in computation field. In order to describe branched cracks, it is necessary to set up the additional enrichment. Here we have developed two kinds of branched elements, namely the “element crossed by two separated cracks” and “element embedded by a junction”. Another series of enriched degrees of freedom are introduced to seize the additional discontinuity in the elements. A shifted enrichment scheme is used to avoid the treatment of blending element. Correspondingly a new mass lumping method is developed for the branched elements based on the kinetic conservation. The derivation of the mass matrix of a four-node quadrilateral element which contains two strong discontinuities is specially presented. Then by choosing crack speed as the branching criterion, the branching process of a single mode I crack is simulated. The results including the branching angle and propagation routes are compared with that obtained by the conventionally used element deletion method.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 11372157 and The Special Research Grant for Doctor Discipline by Ministry of Education of China under Grant No. 20120002110075

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Authors and Affiliations

  1. Applied Mechanics laboratory, Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing , 100084, China

    Dandan Xu, Zhanli Liu, Qinglei Zeng & Zhuo Zhuang

  2. LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing , 100190, China

    Xiaoming Liu

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  1. Dandan Xu
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  2. Zhanli Liu
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  3. Xiaoming Liu
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  4. Qinglei Zeng
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  5. Zhuo Zhuang
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Correspondence to Zhanli Liu or Zhuo Zhuang.

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Xu, D., Liu, Z., Liu, X. et al. Modeling of dynamic crack branching by enhanced extended finite element method. Comput Mech 54, 489–502 (2014). https://doi.org/10.1007/s00466-014-1001-9

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