Scaling Transformations in Solid Mechanics

  • Feodor M. Borodich
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


First a brief historical overview of the development of scaling methods is given. Then it is argued that scaling in solid mechanics should not be restricted to just the equivalence of dimensionless parameters characterising the problem under consideration. A wealth of scaling approaches to solid mechanics is demonstrated on problems of contact and fracture mechanics. It is considered dimensional analysis and classic self-similarity, solutions described by quasi-homogeneous functions, statistical self-similarity, discrete self-similarity, parametric-homogeneity, and mathematical and physical fractals. It is shown that all these scalings are based on the use of either continuous or discrete groups of dilation of coordinates.


Self-similarity parametric-homogeneity statistical scaling fractals 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Feodor M. Borodich
    • 1
  1. 1.Cardiff University School of EngineeringUnited Kingdom

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