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International Journal of Fracture

, Volume 128, Issue 1–4, pp 271–276 | Cite as

Fractal models in fracture mechanics

  • Arseny Kashtanov
  • Yuri Petrov
Article

Abstract

Application of fractal geometry to the problems of fracture mechanics is discussed. Fractal generalization of the energy balance equation to the case of non-square root singularities of the stress field is proposed. Analysis of the fracture at the sharp angular notch in a plate on the basis of the generalized energy balance equation is performed. Good corroboration between the suggested approach and experiments is observed.

Keywords

Fracture Surface Fractal Dimension Critical Loading Fracture Process Fractal Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Kashtanov, A.V. and Petrov, Y.V. (2001). Fractal Generalization of the Energy Balance Equation in a Linear Fracture Mechanics, SPbSU, St.-Petersburg, (In Russian).Google Scholar
  2. Mandelbrot, B.B. (1983). The Fractal Geometry of Nature. Freeman, New York.Google Scholar
  3. Morozov, N.F. (1984). Mathematical Problems of a Crack Theory. Nauka, Moscow, (In Russian).Google Scholar
  4. Panin, V.E., Grinyaev, Y.V. and Danilov, V.E. etc. (1990). Structural Levels of Plastic Deformation and Fracture. Nauka, Novosibirsk, (In Russian).Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Arseny Kashtanov
    • 1
  • Yuri Petrov
    • 1
  1. 1.Elasticity DepartmentSt.-Petersburg State University, Mathematics and Mechanics FacultySt.-PetersburgRussia

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