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Likely equilibria of the stochastic Rivlin cube

Mihai, L. Angela ORCID:, Woolley, Thomas E. ORCID: and Goriely, Alain 2019. Likely equilibria of the stochastic Rivlin cube. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377 (2144) , 20180068. 10.1098/rsta.2018.0068

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The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the purely elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Additional Information: Published by the Royal Society under the terms of the Creative Commons Attribution License by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Publisher: The Royal Society
ISSN: 1364-503X
Date of First Compliant Deposit: 25 June 2018
Date of Acceptance: 25 June 2018
Last Modified: 23 Oct 2022 14:05

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