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Stochastic modelling and analysis of homogeneous hyperelastic solids

Fitt, Danielle 2020. Stochastic modelling and analysis of homogeneous hyperelastic solids. PhD Thesis, Cardiff University.
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Combining finite elasticity and information theory, a stochastic method is devel oped in order to accurately predict and assess the behaviour of materials, and also to model experimental data. An explicit strategy to calibrate homogeneous isotropic hyperelastic models to mean values and the standard deviation of ei ther the stress-strain function or the nonlinear shear modulus is devised, and the technique of using Bayes Theorem to select the optimal model to represent the ma terial or data in question is presented, specifically here in relation to manufactured silicone specimens. An analysis of the behaviour of solid materials under various deformations, including necking instability, the inflation of cylindrical tubes and spheres, and the cavitation of spherical shells, when the material is stochastic, is demonstrated, before an extension to the dynamic finite deformations of stochastic hyperelastic solids, including the shear motion of a cuboid, the quasi-equilibrated radial-axial motion of a cylindrical tube, and the quasi-equilibrated radial motion of a spherical shell, is explored. Ultimately, it is determined that the amplitude and period of oscillation of stochastic bodies are characterised by probability dis tributions. Overall, the aim is to highlight the need for mathematical modelling to consider the variability obtained in experimental data, in the mechanical re sponses of materials, or in testing protocols, with a view to enhancing the accuracy of the mathematical modelling techniques employed, and, as a result, to provide an improved assessment or prediction of the behaviour of the materials in question.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Date of First Compliant Deposit: 20 October 2020
Last Modified: 21 Oct 2020 09:28

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