Likely equilibria of stochastic hyperelastic spherical shells and tubes
arXiv:1808.02110 · doi:10.1177/1081286518811881
The paper studies how randomness in material properties affects the inflation stability of elastic spherical shells and cylindrical tubes, deriving probability distributions for when internal pressure increases monotonically with stretch.
Abstract
In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter.
arXiv admin note: text overlap with arXiv:1808.01263