Numerical factorization of a matrix-function with exponential factors in an anti-plane problem for a crack with process zone

P. Livasov*, G. Mishuris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
87 Downloads (Pure)

Abstract

In this paper, we consider an interface mode III crack with a process zone located in front of the fracture tip. The zone is described by imperfect transmission conditions. After application of the Fourier transform, the original problem is reduced to a vectorial Wiener- Hopf equation whose kernel contains oscillatory factors. We perform the factorization numerically using an iterative algorithm and discuss convergence of the method depending on the problem parameters. In the analysis of the solution, special attention is paid to its behaviour near both ends of the process zone. Qualitative analysis was performed to determine admissible values of the process zone's length for which equilibrium cracks exist.

Original languageEnglish
Article number20190109
Number of pages16
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume377
Issue number2156
Early online date02 Sept 2019
DOIs
Publication statusPublished - 21 Oct 2019

Keywords

  • Fracture
  • Matrix factorization
  • Process zone
  • Wiener-Hopf method

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