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Likely oscillatory motions of stochastic hyperelastic solids

Mihai, L.A., Fitt, Danielle, Woolley, Thomas and Goriely, Alain 2019. Likely oscillatory motions of stochastic hyperelastic solids. Transactions of Mathematics and Its Applications 3 (1) , tnz003. 10.1093/imatrm/tnz003

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Abstract

Stochastic homogeneous hyperelastic solids are characterized by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney–Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterized. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as ‘likely oscillatory motions’.

Item Type: Article
Date Type: Publication
Status: In Press
Schools: Mathematics
Publisher: Oxford University Press
ISSN: 2398-4945
Related URLs:
Date of First Compliant Deposit: 16 April 2019
Date of Acceptance: 16 April 2019
Last Modified: 05 Sep 2019 08:17
URI: http://orca.cf.ac.uk/id/eprint/121807

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