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The Logistic Map and the Route to Chaos pp 295–316Cite as

A Chaos and Fractal Dynamic Approach to the Fracture Mechanics

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Part of the book series: Understanding Complex Systems ((UCS))

Summary

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.

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Author information

Authors and Affiliations

  1. GTEME - Grupo de Termodinâmica, Mecânica e Eletrônica dos Materiais, Brasil

    Lucas Máximo Alves

  2. Departamento de Engenharia de Materiais, Universidade Estadual de Ponta Grossa, Caixa Postal 1007, Av. Gal. Carlos Calvalcanti, 4748, Campus UEPG/Bloco L - Uvaranas, Ponta Grossa, Paraná, CEP. 84030.000, Brasil

    Lucas Máximo Alves

  3. Grupo de Nanotecnologia e Ciência a Nano-Escala, Portugal

    Rui F.M. Lobo

  4. Departamento de Física, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Rui F.M. Lobo

Authors
  1. Lucas Máximo Alves
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  2. Rui F.M. Lobo
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Editor information

Editors and Affiliations

  1. Institut de Physique, Université de Liège, B5, Sart Tilman, 4000, Liège, Belgium

    Marcel Ausloos

  2. Royal Military Academy/ELEC, Avenue de la, Renaissancelaan 30, 1000, Brussels, Belgium

    Michel Dirickx

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© 2006 Springer-Verlag Berlin Heidelberg

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Alves, L.M., Lobo, R.F. (2006). A Chaos and Fractal Dynamic Approach to the Fracture Mechanics. In: Ausloos, M., Dirickx, M. (eds) The Logistic Map and the Route to Chaos. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32023-7_17

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