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IUTAM Symposium on Scaling in Solid Mechanics pp 11–26Cite as

Scaling Transformations in Solid Mechanics

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Part of the book series: Iutam Bookseries ((IUTAMBOOK,volume 10))

Abstract

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.

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Author information

Authors and Affiliations

  1. Cardiff University School of Engineering, Cardiff CF24 3AA, United Kingdom

    Feodor M. Borodich

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  1. Feodor M. Borodich
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Editors and Affiliations

  1. School of Engineering, Cardiff University, Queen’s Bldg., The Parade, Cardiff CF24 3AA, UK

    F.M. Borodich (borodichfm@cardiff.ac.uk) (borodichfm@cardiff.ac.uk)

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Borodich, F.M. (2009). Scaling Transformations in Solid Mechanics. In: Borodich, F. (eds) IUTAM Symposium on Scaling in Solid Mechanics. Iutam Bookseries, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9033-2_2

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  • DOI: https://doi.org/10.1007/978-1-4020-9033-2_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9032-5

  • Online ISBN: 978-1-4020-9033-2

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