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Likely equilibria of stochastic hyperelastic spherical shells and tubes

Mihai, L. Angela, Fitt, Danielle, Woolley, Thomas E. and Goriely, Alain 2019. Likely equilibria of stochastic hyperelastic spherical shells and tubes. Mathematics and Mechanics of Solids 24 (7) , pp. 2066-2082. 10.1177/1081286518811881

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: SAGE
ISSN: 1081-2865
Date of First Compliant Deposit: 17 October 2018
Date of Acceptance: 17 October 2018
Last Modified: 26 Nov 2020 04:51

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