Summary
The previously derived expressions for the incremental elastic coefficients of an isotropic medium under initial stress are applied to rubbertype elasticity. As a corollary an exact theory is obtained for the surface instability of such material under compression. It is found that in plane strain the incremental properties remain isotropic and are characterized by a single strain-dependent modulus. In three-dimensional strain the elastic properties are found to coincide with those of the elastic medium introduced by Green to illustrate the properties of electromagnetic propagation. The apparent rigidity of the surface as a function of strain is evaluated and is shown to result from the combined effect of the variation of rigidity modulus and a membrane effect due to the initial stress. At a critical compression the two effects act in opposite directions and the apparent surface rigidity vanishes causing incipient instability.
The phenomenon is formally analogous to Rayleigh waves. Attention is also called to the existence of interfacial instability at a surface of discontinuity of two elastic media under initial stress in analogy with Stoneley waves.
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References
Biot, M. A., Ann. Soc. Scient. Bruxelles54B (1934) 18.
Biot, M. A., Theory of Elasticity with Large Displacements and Rotations, Proc. Fifth Intern. Congr. Appl. Mech. 1938.
Biot, M. A., Phil. Mag.27 (1939) 468.
Biot, M. A., Quart. Appl. Math.XVII (1959) 185.
Treloar, L. R. G., Large Elastic Deformation in Rubberlike Materials — Deformation and Flow of Solids, IUTAM Colloquium Madrid, 1955, Springer, Berlin, 1956.
Cifferi, A. and P. J. Flory, J. Appl. Phys.30 (1959) 1498.
Biot, M. A., Appl. sci. Res.A12 (1963) 151.
Green, G., Cambridge Phil. Soc. Trans.7 (1839) or Mathematical Papers London, 1871, p. 293.
Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity. Fourth Edition Cambridge University Press, 1927 (Reprinted by Dower Publications New York 1944), p. 299.
Biot, M. A., J. Appl. Phys.11 (1940) 522.
Biot, M. A. and H. Odé, Quart. Appl. Math.XIX (1962) 351.
Biot, M. A., J. Franklin Inst.270 (1960) 190.
Biot, M. A., Stability Problems of Inhomogeneous Yiscoolastic Media, Proc. IUTAM Colloqui um on Non-homogeneity in Elasticity and Plasticity, Warsaw 1953, Pergamon Press, pp. 311–321.
Buckens, F., Ann. Geofis.XI (1958) 99.
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This work was supported by the Air Force Office of Scientific Research under contract No. AF 49(638)-337. The contents of this paper were included in AFOSR Report No. 1771 of November 1961.
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BIOT, M.A. Surface instability of rubber in compression. Appl. sci. Res. 12, 168–182 (1963). https://doi.org/10.1007/BF03184638
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DOI: https://doi.org/10.1007/BF03184638