On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions

Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole

“…The uniform electric current j y with δ = π/2 causes the uniform magnetic field H x at the remote field of which direction is that of the x axis. This result coincides with the result of [21,6] where H 0 = j 0 (1 + h/a)z. Figures 8 and 9 show the stress distributions of stress state (b).…”

“…Substituting (17) into (18), a bi-harmonic equation is obtained. When the components of the mechanical elastic stress,σ x , σ y , τ xy , are substituted into the compatibility equation, the homogenous bi-harmonic equation is also obtained since the magnetic field intensities H x (x, y, z), H y (x, y, z) are harmonic functions, and the same result is obtained [6].…”

“…Thus, it becomes important to study the effects of the magnetic field on the singular behavior of stress near the tip of any cracks. Some reviews for magneto-solid mechanics were given by Paria [1], Moon [2,3], Pao [4], Liang et al [5] and Hasebe et al [6]. There are some models for the magnetic stress analysis for soft ferromagnetic materials, i.e., Maxwell stress, pole, dipole, and Ampere current models [2,3].…”

“…Intensities of the magnetic field component and stress intensity factors at the crack tip are obtained and the magnitude is investigated for a steel plate as an example. Hasebe et al [6,21] analyzed the magnetic stress in an infinite plate containing a square hole with an edge crack, or an arbitrary hole subjected to the uniform magnetic field at the remote field. The relation between the magnetic stress analysis of [6,21] subjected to the given magnetic field and the analysis of this paper subjected to electric current is also stated.…”

Modelling of Magnetosensitive Elastomers

“…In these weak-coupling models the magnetic equations and the mechanical equations are solved separately. More accurate linear elastic models, based on the strong coupling, solve simultaneously the governing equations of the problem (Belahcen, 2004, Hasebe et al, 2007, Zhou & Wang, 2006a. However, elastomers exhibit strongly nonlinear elastic behaviour and undergo large deformations.…”