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An XFEM/Spectral element method for dynamic crack propagation

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Abstract

A high-order extended finite element method based on the spectral element method for the simulation of dynamic fracture is developed. The partition of unity for the discontinuous displacement is constructed by employing p order spectral element. This method shows great advantages in the simulations of moving crack and mixed mode crack. The numerical oscillations are effectively suppressed and the accuracy of computed stress intensity factors and crack path are improved markedly. Furthermore the simulation results show that p-refinement is more effective in improving the stress contour near the crack tip than h-refinement. The well known form of the explicit central difference method is used and the critical time step for this method is investigated. We find that by using lumped mass matrix the critical time step Δt c for this high-order extended finite element is almost independent of the crack position.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208-3111, USA

    Z. L. Liu, T. Menouillard & T. Belytschko

Authors
  1. Z. L. Liu
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  2. T. Menouillard
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  3. T. Belytschko
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Correspondence to T. Belytschko.

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Liu, Z.L., Menouillard, T. & Belytschko, T. An XFEM/Spectral element method for dynamic crack propagation. Int J Fract 169, 183–198 (2011). https://doi.org/10.1007/s10704-011-9593-y

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  • DOI: https://doi.org/10.1007/s10704-011-9593-y

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