Nonlinear Dynamical Analysis of Cavitation in Anisotropic Incompressible Hyperelastic Spheres under Periodic Step Loads
X.G. Yuan; and H.W. Zhang

doi:10.3970/cmes.2008.032.175
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 32, No. 3, pp. 175-184, 2008
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Keywords Incompressible hyperelastic material; motion equation of void; nonlinear periodic vibration; constant load; periodic step loads
Abstract In this paper, a dynamic problem that describes void formation and motion in an incompressible hyperelastic solid sphere composed of a transversely isotropic Valanis-Landel material is examined, where the sphere is subjected to a class of periodic step tensile loads on its surface. A motion equation of void is derived. On analyzing the dynamical properties of the motion equation and examining the effect of material anisotropy on void formation and motion in the sphere, we obtain some new and interesting results. Firstly, under a constant surface tensile load, it is proved that a void would form in the sphere as the tensile load exceeds a certain critical value and that the motion of the formed void with time would present a class of singular period oscillations, the oscillation center is also determined. Secondly, under periodic step tensile loads, the existence conditions for periodic oscillation of the formed void are presented.
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