By Krasnov N.F.
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Extra resources for Aerodynamics part 2. Methods of aerodynamic calculations
14. R. Burridge and L. Knopoﬀ, Bull. Seis. Soc. Am. 57 341–371 (1967). 15. M. S. Langer, Phys. Rev. Lett. M. S. E. Shaw, Rev. Mod. Phys. 66 657–670 (1994); G. Ananthakrishna and H. Ramachandran in Nonlinearity and Breakdown in Soft Condensed Matter, Eds. K. K. Chakrabarti and A. Hansen, LNP 437, Springer Verlag, Heidelberg (1994); T. Mori and H. Kawamura, Phys. Rev. Letts. 94 058501 (2005). 16. P. Bak, How Nature Works, Oxford University Press, Oxford (1997). 17. K. B. Stinchcombe, Physica A 270 27 (1999); S.
We then consider the distribution of contact areas, as one fractal surface slides over the other. K. Chakrabarti total contact area between the two surfaces to be proportional to the elastic strain energy that can be grown during the sticking period, as the solid–solid friction force arises from the elastic strains at the contacts between the asperities. We then consider this energy to be released as one surface slips over the other and sticks again to the next contact or overlap between the rough surfaces.
It ﬁnally drops to zero discontinuously by an amount σf∗ U ∗ (σf ) = 1/[4(1 − σL )] = σf at the breaking point σ = σf or δ = σf∗ /κ = 1/2κ for the bundle. This indicates that the stress drop at the ﬁnal failure point of the bundle is related to the extent (σL ) of the linear region of the stress–strain curve of the same bundle. S 1 _____ L 0 __L 1 __ 2 Fig. 6. Schematic stress (S)–strain (δ) curve of the bundle (shown by the solid line), following (20), with the ﬁbre strength distribution (17) (as shown in Fig.
Aerodynamics part 2. Methods of aerodynamic calculations by Krasnov N.F.