Engineering Transactions, 8, 2, pp. 275-291, 1960

Kołowo-Symetryczne i Płaskie Ścinanie Łączników Gumowych w Świetle Nieliniowej Teorii Sprężystości

S. Zahorski
Instytut Podstawowych Problemów Techniki PAN

Two cases of rubber elements are considered as shown at Figs 1a and 16 the deformation schemes being shown at Figs. 2 and 4. Such elements find application in motor-car and aircraft engineering. The considerations are based on the assumption of static load and a more general form of the elastic potential than is used in other works concerning rubber-like materials. This potential, discussed in greater detail in the author's paper, [8], depends on three material constants (2.1).
Using A. E. GREEN's method and, to a considerable extent, the notations of the Ref. [2], the contravariant tensor is given in the form (2.4) for axially symmetric shear, and in the form (7.7) for plane shear. Normal and shear stresses appearing in the surfaces of the elements are determined by (5.3), (5.5) and (7.8), (7.9). Relations (5.7), (7.10) between the unit force S and the corresponding displacement wo (or its derivative w') are established. The relations obtained are formally in agreement with the solutions obtained by R. S. RIVLIN and A. E. GREEN, as confined to the case of material characterized by the familiar formula of MOONEY (cf. [7]). Two different variants of the solution are discussed, depending on the
sign of the material constant k determined by (2.9).
In the final part, graphs illustrate the relations (5.7) and (7.10) for two real materials. Figs. 6 and 7 concern circularly-symmetric shear, and Fig. 8 plane shear. The theoretical curves obtained are confronted with the results of experiments carried out by other investigators. Good qualitative agreement is found. In the case of plane shear, Fig. 8, the agreement between the experimental points and the theoretical curve is also good.

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[in Russian]

A. E. GREEN, W. ZERNA, Theoretical Elasticity, Oxford 1954.

E.F. GÖBEL, Gummifedern, Berlin-Göttingen-Heidelberg 1955.

A. ISHIHARA, N. HASHITSUME, M. TATIBANA, Statistical Theory of Rubber-Like Elasticity, J. Chem. Phys., 19 (1951).

Z. JAŚKIEWICZ, Elementy pojazdów mechanicznych. Łączniki sprężyste, Warszawa 1959.

R.S. RIVLIN, Philos. Trans., A240, 459, 491 (1948). [7] L. TRELOAR, The Physics of Rubber Elasticity, Oxford 1949.

S. ZAHORSKI, A Form of Elastic Potential for Rubber-Like Materials, Arch. Mech. Stos., 5,10 (1959).