Likely cavitation and radial motion of stochastic elastic spheres 1: Driven by dead-load traction
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The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the elastic parameters are characterised by probability density functions. Specifically, we consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stochastic neo-Hookean phases, and inhomogeneous spheres of neo-Hookean-like material with a radially varying parameter. When these spheres are subject to a uniform tensile surface dead load in the radial direction, we show that the material at the centre determines the critical load at which a spherical cavity forms there. However, while supercritical bifurcation, with stable cavitation, is always obtained in a static sphere of stochastic neo-Hookean material, for the composite and radially inhomogeneous spheres, a subcritical bifurcation, with snap cavitation, is also possible. For the dynamic spheres under suitable dead-load traction, oscillatory motions are produced, such that a cavity forms and expands to a maximum radius, then collapses again to zero and repeats the cycle. As the material parameters are non-deterministic, the results are characterised by probability distributions.
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