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Radially symmetric cavitation for hyperelastic materials. (English) Zbl 0588.73021
This paper considers the question of existence of a class of singular radial solutions to the equilibrium equations of nonlinear elasticity. The solutions form a spherical hole in a ball of isotropic material, induced by pulling the ball radially outwards (displacement or traction boundary conditions). Variational methods previously used by J. Ball [Philos. Trans. R. Soc. Lond., A 306, 557-611 (1982; Zbl 0513.73020)] to study the same problem are here replaced by the shooting method, which is simpler. As a result there is some generalization in the form of the constitutive assumptions which describe the material making up the ball. This comes at a cost of losing information concerning stability within the class of radial solutions. The general problem of stability still appears open.
Reviewer: R.Saxton

MSC:
74B20 Nonlinear elasticity
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References:
[1] Ball, J. M., Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. Lond., A306, 557-611, (1982) · Zbl 0513.73020
[2] Gurtin, M. E., Topics in finite elasticity, S. I. A. M. Region Conference Series, n^o 35, (1981), Philadelphia
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