On wave propagation in finitely deformed magnetoelastic solids

Saxena, Prashant (2012) On wave propagation in finitely deformed magnetoelastic solids. PhD thesis, University of Glasgow.

Abstract

In this thesis we consider some boundary value problems concerning nonlinear deformations and incremental motions in magnetoelastic solids. Three main problems have been addressed relating to waves propagating on the surface of a finitely deformed half-space and waves propagating along the axis of a thick-walled tube.

First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a ``total'' isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic field.

In the first problem, we analyze the propagation of Rayleigh-type surface waves for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. Numerical results for a Mooney--Rivlin type magnetoelastic material show that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field. A magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

In the second problem, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space is analyzed for a Mooney--Rivlin type and a neo-Hookean type magnetoelastic energy function. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein--Gulyaev waves in piezoelectric materials.

Then, we consider nonlinear axisymmetric deformations and incremental motions of a cylindrical magnetoelastic tube. The effects of internal pressure, axial stretch, and magnetic field are studied for two different kinds of energy density functions. It is found that in general an underlying azimuthal magnetic field increases the total internal pressure, affects the axial load, and induces stability in the tube. Dependence of the incremental motion on internal pressure, axial stretch, thickness of tube, and the applied magnetic field is illustrated graphically.

Finally, we consider the general equations of Electrodynamics and Thermodynamics in continua. In particular, we write the equations governing mechanical waves, electromagnetic fields and temperature changes in a magnetoelastic conductor with a motivation to describe the electromagnetic acoustic transduction (EMAT) process. This is a work in progress and an open research problem for the future.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Chapter 3 published as -- Saxena, P. and Ogden, R. W. (2011). On surface waves in a finitely deformed magnetoelastic half-space. International Journal of Applied Mechanics, 3(4):633–665. Chapter 4 published as -- Saxena, P. and Ogden, R.W., On Love-type waves in a finitely deformed magnetoelastic layered half-space. Zeitschrift für Angewandte Mathematik und Physik, doi: 10.1007/s00033-012-0204-1.
• Keywords: Nonlinear magnetoelasticity, nonlinear elasticity, wave propagation, finite deformation, solid mechanics, magnetorheological elastomer
• Subjects: Q Science > QC Physics; Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Ogden, Professor Ray W.
• Date of Award: 2012
• Depositing User: Prashant Saxena
• Unique ID: glathesis:2012-3611
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 02 Oct 2012
• Last Modified: 10 Dec 2012 14:09
• URI: https://theses.gla.ac.uk/id/eprint/3611