Scaling transformations in solid mechanics

Borodich, Feodor M. ORCID: https://orcid.org/0000-0002-7935-0956 2007. Scaling transformations in solid mechanics. Presented at: IUTAM Symposium on Scaling in Solid Mechanics, Cardiff, UK, 25-29 June 2007. Published in: Borodich, Feodor M. ed. IUTAM Symposium on Scaling in Solid Mechanics:proceedings of the IUTAM Symposium held in Cardiff, UK, 25-29 June, 2007. Proceedings of the IUTAM Symposium on Scaling in Solid Mechanics. IUTAM Bookseries (10) Springer, pp. 11-26. 10.1007/978-1-4020-9033-2_2

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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.

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Publication
Status:	Published
Schools:	Engineering
Uncontrolled Keywords:	Self-similarity ; Parametric-homogeneity ; Statistical scaling ; fractals.
Publisher:	Springer
ISBN:	9781402090325
Last Modified:	17 Oct 2022 10:18
URI:	https://orca.cardiff.ac.uk/id/eprint/7651

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