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The shifted fracture method

Publication ,  Journal Article
Li, K; Atallah, NM; Rodríguez-Ferran, A; Valiveti, DM; Scovazzi, G
Published in: International Journal for Numerical Methods in Engineering
November 30, 2021

We propose a new framework for fracture mechanics, based on the idea of an approximate fracture geometry representation combined with approximate interface conditions. Our approach evolves from the shifted interface method, and introduces the concept of an approximate fracture surface composed of the full edges/faces of an underlying grid that are geometrically close to the true fracture geometry. The original interface conditions are then modified on the surrogate fracture geometry, by way of Taylor expansions. The shifted fracture method does not require cut cell computations or complex data structures, since the behavior of the true fracture is mimicked with standard integrals on the approximate fracture surface. Furthermore, the energetics of the true fracture are represented within the accuracy of the underlying polynomial finite element approximation and independently of the grid topology. The computational framework is presented here in its generality and then applied in the specific context of cohesive zone models, with an extensive set of numerical experiments in two and three dimensions.

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Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

November 30, 2021

Volume

122

Issue

22

Start / End Page

6641 / 6679

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

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Li, K., Atallah, N. M., Rodríguez-Ferran, A., Valiveti, D. M., & Scovazzi, G. (2021). The shifted fracture method. International Journal for Numerical Methods in Engineering, 122(22), 6641–6679. https://doi.org/10.1002/nme.6806
Li, K., N. M. Atallah, A. Rodríguez-Ferran, D. M. Valiveti, and G. Scovazzi. “The shifted fracture method.” International Journal for Numerical Methods in Engineering 122, no. 22 (November 30, 2021): 6641–79. https://doi.org/10.1002/nme.6806.
Li K, Atallah NM, Rodríguez-Ferran A, Valiveti DM, Scovazzi G. The shifted fracture method. International Journal for Numerical Methods in Engineering. 2021 Nov 30;122(22):6641–79.
Li, K., et al. “The shifted fracture method.” International Journal for Numerical Methods in Engineering, vol. 122, no. 22, Nov. 2021, pp. 6641–79. Scopus, doi:10.1002/nme.6806.
Li K, Atallah NM, Rodríguez-Ferran A, Valiveti DM, Scovazzi G. The shifted fracture method. International Journal for Numerical Methods in Engineering. 2021 Nov 30;122(22):6641–6679.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

November 30, 2021

Volume

122

Issue

22

Start / End Page

6641 / 6679

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering