The Mathematical Institute, University of Oxford, Eprints Archive

Elastic wave scattering from a strained region

Parnell, W. (2000) Elastic wave scattering from a strained region. Masters thesis, University of Oxford.

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Abstract

This dissertation considers elastic wave scattering from a micro-sphere embedded in a rubber substrate which has been initially strained. Its aim is to ascertain the extent to which the strained region affects the scattering process.

It is proposed that under hydrostatic loading a micro-sphere will compress nonlinearly. This is justified by calculating the compressed radius of a micro-sphere for different forms of the stored energy function corresponding to linear and nonlinear elasticity. It is shown that linear elasticity, as used in current TMSL models, predicts that the micro-sphere compresses to a smaller radius than that predicted by standard nonlinear elastic models of rubber-like materials.

The initial strain modifies the Lame moduli and therefore further experimental work is necessary in order to calculate the full equations of motion for small displacements superposed on top of the initial finite strain. Without this further experimental knowledge the equations are correct only to leading order.

The low frequency scattering problem is solved at leading order so that we can ascertain how monopole scattering is affected by the strained region. It is shown that the monopole scattering cross section for scattering from a spherical cavity in a strained region is three orders of magnitude smaller than that for an isotropic region. Hence, the scattering process is significantly affected by the strained region.

Two modifications to the current TMSL model are proposed. Firstly, the prediction of the compressed radius should be made according to nonlinear elasticity. Secondly, scattering effects due to the strained region should be included in the model since they contribute significantly to the scattering process.

Item Type:Thesis (Masters)
Subjects:H - N > Mechanics of deformable solids
O - Z > Partial differential equations
H - N > Numerical analysis
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:14
Deposited By:Eprints Administrator
Deposited On:03 Mar 2004
Last Modified:20 Jul 2009 14:12

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