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Stochastic finite strain analysis of inhomogeneous hyperelastic solids

Alamoudi, Manal 2022. Stochastic finite strain analysis of inhomogeneous hyperelastic solids. PhD Thesis, Cardiff University.
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This thesis presents a theoretical study of static and dynamic inflation, and finite amplitude oscillatory motion of inhomogeneous spherical shells and cylindrical tubes of stochastic hyperelastic material. These bodies are deformed by radially symmetric uniform inflation, and, in the dynamic case, are subject to either a surface dead load or an impulse traction, applied uniformly in the radial direction. We consider composite shells and tubes with two concentric stochastic homogeneous neo-Hookean phases, and inhomogeneous bodies of stochastic neo-Hookean material with constitutive parameters varying continuously in the radial direction. For the homogeneous materials, we define the elastic parameters as spatially-independent random variables, while for the radially inhomogeneous bodies, we take the parameters as spatially-dependent random fields, described by Gamma probability density functions. Under radially symmetric dynamic deformation treated as quasi-equilibrated motion, we show that these bodies oscillate, i.e., their radius increases up to a point, then decreases, then increases again, and so on, and the amplitude and period of the oscillations are characterised by probability distributions, depending on the initial conditions, geometry, and the probabilistic material properties.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Date of First Compliant Deposit: 27 May 2022
Last Modified: 14 Dec 2022 02:28

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