Open Access

ARTICLE

Nonlinear Dynamical Analysis in Incompressible Transversely Isotropic Nonlinearly Elastic Materials: Cavity Formation and Motion in Solid Spheres

X.G. Yuan¹, R.J. Zhang²

1 Department of Mathematics and Information Science, Yantai University, Yantai 264005 Shandong, P.R. China, yxg1971@163.com.
2 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P.R. China.

Computers, Materials & Continua 2006, 3(3), 119-130. https://doi.org/10.3970/cmc.2006.003.119

Abstract

In this paper, the problem of cavity formation and motion in an incompressible transversely isotropic nonlinearly elastic solid sphere, which is subjected to a uniform radial tensile dead load on its surface, is examined in the context of nonlinear elastodynamics. The strain energy density associated with the nonlinearly elastic material may be viewed as the generalized forms of some known material models. It is proved that some determinate conditions must be imposed on the form of the strain energy density such that the surface tensile dead load has a finite critical value. Correspondingly, as the surface tensile dead load exceeds the critical value, a cavity would form in the interior of the sphere and the motion of the formed cavity with time would present a class of singular nonlinear periodic oscillations. The effects of constitutive parameters on cavity formation and motion are discussed in detail, and the corresponding numerical examples are given simultaneously.

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Keywords

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