Mathematical modelling of non-linear magneto- and electro-active rubber-like materials

Bustamante, Roger (2007) Mathematical modelling of non-linear magneto- and electro-active rubber-like materials. PhD thesis, University of Glasgow.

Abstract

Three main problems have been addressed: universal relations, the modelling of transversely isotropic magneto- and electro-active elastomers, and the variational formulation.

The complete setoff linear universal relations was found for isotropic magneto- and electro-active elastomers. Some universal relations for some special simplified cases of the constitutive equations were also found. Two non-linear universal relations were studied, for the helical shear and for the anti-plane shear deformations.

Two boundary value problems were solved using the finite difference method: one of them was the inflation and extension of a tube of finite length under the influence of a uniform axial magnetic field applied far away, and the other was the uniform extension of a cylinder with an electric field applied far away.

The constitutive equations for transversely isotropic magneto- and electro-active elastomers were developed, and several simple boundary value problems were solved. For the case of transversely isotropic magneto-active elastomers a preliminary form for the energy function was proposed.

Finally simple variational formulations for the magneto-elastic problem were found, and an extension of these formulations, which takes into account the interaction with a rigid semi-infinite body was proposed.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Ogden, Prof. Ray
• Date of Award: 2007
• Depositing User: Elaine Ballantyne
• Unique ID: glathesis:2007-2096
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 15 Sep 2010
• Last Modified: 10 Dec 2012 13:51
• URI: https://theses.gla.ac.uk/id/eprint/2096