A chaos and fractal dynamic approach to the fracture mechanics

Lucas Máximo Alves, Rui F. M. Lobo

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

It is shown that the onset of instabilities observed in the fracture of brittle isotropic materials is a consequence of the mathematical structure of chaos that underlies such phenomena. The straight line crack velocity is written in the form of a logistic map explaining the onset of instabilities observed by Fineberg et al. This approach provides a single and concise tool to study this and other nonlinear aspects presented by dynamic crack growth.

Original languageEnglish
Title of host publicationThe Logistic Map and the Route to Chaos: From The Beginnings to Modern Applications
EditorsMarcel Ausloos, Michel Dirickx
Place of PublicationBerlin, Heidelberg
PublisherSpringer-Verlag
Pages295-316
Number of pages22
ISBN (Electronic)978-3-540-32023-4
ISBN (Print)978-3-540-28366-9
DOIs
Publication statusPublished - 1 Dec 2006

Publication series

NameUnderstanding Complex Systems
PublisherSpringer-Verlag
Volume2006
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840

Keywords

  • Crack Length
  • Energy Release Rate
  • Process Zone
  • Dynamic Fracture
  • Crack Velocity

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