Likely cavitation and radial motion of stochastic elastic spheres 2: Impulse driven

TL;DR

This paper investigates the static and dynamic cavitation behavior of stochastic elastic spheres under impulse traction, revealing how randomness in material properties affects cavitation thresholds and bifurcation types.

Contribution

It extends previous work by analyzing stochastic elastic spheres under impulse loading, highlighting differences in cavitation responses and bifurcation behavior due to material randomness.

Findings

Critical cavitation load matches homogeneous sphere predictions.

Post-cavitation radial motion is non-oscillatory.

Static stochastic neo-Hookean spheres exhibit subcritical bifurcation.

Abstract

Cavitation in solids can be caused by tensile dead-load traction or impulse traction. The two different types of boundary conditions lead to different static and dynamic solutions. In addition, if the material is stochastic, i.e., the model parameters are represented by probability distributions, the expected behaviour is more complicated to describe. Here, following the first instalment of this work, we examine the static and dynamic cavitation of a stochastic material under a uniform tensile impulse traction in different spherical geometries. We find that the critical load at which a cavity forms at the centre of the sphere is the same as for the homogeneous sphere composed entirely of the material found at its centre, while the post-cavitation radial motion is non-oscillatory. However, there are some important differences in the nonlinear elastic responses. Specifically, subcritical bifurcation, with snap cavitation, is obtained in a static sphere of stochastic neo-Hookean material and also in a radially inhomogeneous sphere, whereas for composite spheres, a supercritical bifurcation, with stable cavitation, is possible as well. Given the non-deterministic material parameters, the results are characterised by probability distributions.