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