On the general governing equations of electromagnetic acoustic transducers

In this paper, we present the general governing equations of electrodynamics and continuum mechanics that need to be considered while mathematically modelling the behaviour of electromagnetic acoustic transducers (EMATs). We consider the existence of finite deformations for soft materials and the possibility of electric currents, temperature gradients, and internal heat generation due to dissipation. Starting with Maxwell's equations of electromagnetism and balance laws of nonlinear elasticity, we present the governing equations and boundary conditions in incremental form in order to solve wave propagation problems of boundary value type.Comment: Version 2: Added reference [16] and corrected grammar at a couple of place

Finite deformations and incremental axisymmetric motions of a magnetoelastic tube

A thick-walled circular cylindrical tube made of an incompressible magnetoelastic material is subjected to a finite static deformation in the presence of an internal pressure, an axial stretch, and an azimuthal or an axial magnetic field. The dependence of the static magnetoelastic deformation on the intensity of the applied magnetic �eld is analysed for two different magnetoelastic energy density functions. Then, superimposed on this static con�guration, incremental axisymmetric motions of the tube and their dependence on the applied magnetic field and deformation parameters are studied. In particular, we show that magnetoelastic coupled waves exist only for particle motions in the azimuthal direction. For particle motion in radial and axial directions, only purely mechanical waves are able to propagate when magnetic field is absent. The wave speeds as well as the stability of the tube can be controlled by changing the internal pressure, axial stretch, and applied magnetic field that demonstrates the applicability of magneto-elastomers as wave guides and vibration absorbers

On rate-dependent dissipation effects in electro-elasticity

This paper deals with the mathematical modelling of large strain electro-viscoelastic deformations in electro-active polymers. Energy dissipation is assumed to occur due to mechanical viscoelasticity of the polymer as well as due to time-dependent effective polarisation of the material. Additive decomposition of the electric field $\mathbb{E} = \mathbb{E}_e + \mathbb{E}_v$ and multiplicative decomposition of the deformation gradient $\mathbf{F} = \mathbf{F}_e \mathbf{F}_v$ are proposed to model the internal dissipation mechanisms. The theory is illustrated with some numerical examples in the end

The Management Education (MBA) Challenge a Study of Managerial Competency Needs & how Well MBA's Differentiate

AbstractMBA & Equivalent Courses” are hugely popular among students and corporates. India has the third largest group of B-School applicants after USA and China. (GMAC Report 2012). This surge in interest in MBA Programs has made B schools and management education a significant participant of the economy. These programs claim to build management skills in the participants to serve the corporate world. But a lot of negative feedback from both industry and academia on the direction and outcome of these programs are making it necessary to investigate the issue.The study using primary data collected from 355 Indian managers belonging to a cross section of industry and organizational hierarchy tries to identify key generic managerial competencies that they find most important to successfully perform their managerial role.The research explores whether MBA's show better on these managerial competencies in comparison to Non MBA's while performing their role and found that corporate managers do not find MBA's better equipped than Non MBA's while performing managerial task on most of the competencies

Instabilities in the axisymmetric magnetoelastic deformation of a cylindrical membrane

We study the inflation of a weakly magnetizable isotropic incompressible cylindrical membrane and the effects of an external magnetic field generated by a current carrying wire placed along the axis of cylinder. A variational formulation based on magnetization is used and the computational results obtained by using four elastic constitutive models (neo-Hookean, Mooney–Rivlin, Ogden, and Arruda–Boyce) are studied and compared. Cylinders of various aspect ratios are studied in each case. Our study shows that the external magnetic field alters the elastic limit point, does not lead to equilibrium solutions below certain value of internal pressure, and can give rise to multiple equilibrium states for a given value of pressure. Presence of magnetic limit point, a phenomenon recently reported in the literature is reconfirmed. Magnetic limit point is a state where a further strengthening of the applied magnetic field at a given pressure does not yield any static equilibrium state. In this case it is detected when the cylindrical membrane deflates into the volume enclosed by itself. We also observe a quadratic relation between the defined magnetic energy parameter and the internal pressure at the magnetic limit point. Relaxed form of the strain energy density is used to account for wrinkling in this case of inward inflation. A finite difference method coupled with an arc-length technique is used for the computations and the stability of the solution is determined from the second variation

Limit points in the free inflation of a magnetoelastic toroidal membrane

One common phenomenon native to inflation of membranes is the elastic limit-point instability–a bifurcation point at which the membrane begins to deform enormously at the slightest increase of pressure. In the case of magnetoelastic materials, there is another possible phenomenon which we call magnetic limit-point instability, a state referring to the non-existence of an equilibrium state –either stable or unstable. In this work, we are concerned with such instabilities in an incompressible isotropic magnetoelastic toroidal membrane with an initial circular cross-section. A non-uniform magnetic field is generated using a circular current carrying loop placed inside the membrane in addition to inflation by a uniform hydrostatic pressure. An energy formulation based on magnetization is used to model the magneto-mechanical coupling along with a Mooney-Rivlin constitutive model for the elastic strain energy density. Computations show that the magnetic field strongly influences the location of elastic limit points and in some cases can cause them to vanish. Multiple equilibrium states are obtained as solutions of the governing equations and a criterion based on second variation is employed to determine their stability. Existence and dependence of magnetic limit point on the magnetic field is demonstrated. While the quantitative results obtained here are specific to the toroidal geometry, the deformation behaviour can be generalised to any magnetoelastic membrane

Instabilities in the free inflation of a nonlinear hyperelastic toroidal membrane

Study on an incompressible nonlinear hyperelastic thin-walled toroidal mem- brane of circular cross-section subjected to inflation due to a uniform pressure is conducted in this work. Comparisons are made for three elastic constitutive mod- els (neo-Hookean, Mooney–Rivlin, and Ogden) and for different geometric aspect ratios (ratio of the radius of cross-section to the radius of revolution). A variational approach is used to derive the equations of equilibrium and bifurcation. An analysis of the pressure–deformation plots shows occurrence of the well-known limit point (snap through) instabilities in membrane. Calculations are performed to study the elastic buckling point to predict bifurcation of solution corresponding to loss of symmetry. Tension field theory is employed to study the wrinkling instability that, in this case, typically occurs near the inner regions of tori with large aspect ratios

Buckling of chiral rods due to coupled axial and rotational growth

We present a growth model for special Cosserat rods that allows for induced rotation of cross-sections. The growth law considers two controls, one for lengthwise growth and other for rotations. This is explored in greater detail for straight rods with helical and hemitropic material symmetries by introduction of a symmetry preserving growth to account for the microstructure. The example of a guided-guided rod possessing a chiral microstructure is considered to study its deformation due to growth. We show the occurrence of growth induced out-of-plane buckling in such rods