Radially symmetric cavitation for hyperelastic materials.

*(English)*Zbl 0588.73021This 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 |

##### Keywords:

radially symmetric cavitation; hyperelastic material; nonlinear boundary value problem; singular second order differential equation; class of stored-energy densities; existence; class of singular radial solutions; equilibrium equations; spherical hole in a ball; isotropic material; shooting method##### 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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