Likely cavitation and radial motion of stochastic elastic spheres
Abstract
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 constitutive parameters are characterised by probability density functions. We consider homogeneous spheres of stochastic neoHookean material, composites with two concentric stochastic neoHookean phases, and inhomogeneous spheres of locally neoHookean material with a radially varying parameter. In all cases, we show that the material at the centre determines the critical load at which a spherical cavity forms there. However, while under deadload traction, a supercritical bifurcation, with stable cavitation, is obtained in a static sphere of stochastic neoHookean material, for the composite and radially inhomogeneous spheres, a subcritical bifurcation, with snap cavitation, is also possible. For the dynamic spheres, oscillatory motions are produced under suitable deadload traction, such that a cavity forms and expands to a maximum radius, then collapses again to zero periodically, but not under impulse traction. Under a surface impulse, a subcritical bifurcation is found in a static sphere of stochastic neoHookean material and also in an inhomogeneous sphere, whereas in composite spheres, supercritical bifurcations can occur as well. Given the nondeterministic material parameters, the results can be characterised in terms of probability distributions.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.10514
 Bibcode:
 2019arXiv190610514M
 Keywords:

 Physics  Classical Physics;
 Mathematics  Numerical Analysis
 EPrint:
 arXiv admin note: text overlap with arXiv:1901.06145