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Discontinuous energy minimizers in nonlinear elastostatics: An example of J. Ball revisited. (English) Zbl 0575.73021
[Compare J. M. Ball, Philos. Trans. R. Soc. London, A 306, 557-611 (1982; Zbl 0513.73020).]
Simple direct methods of the calculus of variations, together with mild a priori restrictions of a constitutive nature, are exploited to show that a uniform radial displacement at the boundary fails to induce a homogeneous radial expansion of a compressible elastic ball when the boundary displacement reaches a critical value (of which an explicit lower bound is offered): rather, above the critical value, energy minimizers are radial deformations with a hole at the center, and are accompanied by a stress field with radial stress vanishing, and circumferential stress unbounded, at the surface of the hole.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
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