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Elastic instabilities in rubber. (English) Zbl 1349.74053
Summary: Materials that undergo large elastic deformations can exhibit novel instabilities. Several examples are considered here: development of an aneurysm on inflating a cylindrical rubber tube; non-uniform stretching on inflating a spherical balloon; expansion of small cavities in rubber blocks when they are subjected to a critical amount of triaxial tension or when they are supersaturated with a dissolved gas; wrinkling of the surface of a block at a critical amount of compression; and the sudden formation of “knots” on twisting stretched cylindrical rods. These various deformations are analyzed in terms of simple strain energy functions using Rivlin’s theory of large elastic deformations. The theoretical results are then compared with experimental measurements of the onset of unstable states. Such comparisons provide new tests of Rivlin’s theory and, at least in principle, critical tests of proposed strain energy functions for rubber. Moreover, the onset of highly non-uniform deformations has serious implications for the fatigue life and fracture resistance of rubber components.

MSC:
74B15 Equations linearized about a deformed state (small deformations superposed on large)
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