A magnetoelectroelastic medium with an elliptical cavity under combined mechanical–electric–magnetic loading

Electromagnetoelastic problem for a plate with holes and cracks

“…For a circular ring made of material BaTiO 3 -CoFe 2 O 4 [12,22] and having outer radius r 0 and inner radius r 1 (Fig. 1), Table 4 gives the normal stress s s on area elements perpendicular to boundary, electric-flux density D n and electric-field strength E n on area elements tangential to the boundary, and internal energy density U at some boundary points for different values of r r 1 0 / .…”

“…After the unknown constants and, hence, the unknown complex potentials are found, we can determine the EMES at any point of the plate and, if the plate has cracks, the intensity factors for the stress k 1 , k 2 , electric-flux density k D , magnetic-flux density k B , electric-field strength k E , and magnetic-field strength k H [7,11] We will discuss some of the numerical results obtained for a circular ring made of material BaTiO 3 -CoFe 2 O 4 [12,22] and having outer radius r 0 and inner radius r 1 (Fig. 1) Table 1 collects the values of the normal stress s s on area elements perpendicular to the boundaries and the internal energy densityU at some points of the ring under concentrated forces applied at the centers of the bridges (h r r r = + - / by solving the problems of elasticity (E, electric and magnetic properties disregarded), electroelasticity (EE, magnetic properties disregarded), magnetoelasticity (ME, electric properties disregarded), and electromagnetoelasticity (EME, both electric and magnetic properties allowed for).…”

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

“…Wang and Mai [7] gave the expressions for the energy release rate of piezoelectric/piezomagnetic solids. Zhao et al [8] presented the solution for a crack in a magnetoelectroelastic medium where the permeability to the electric and magnetic fields is considered, and gave the expression of strain energy density factor. Zhou et al [9] obtained the closed form solution of a Mode-I crack in the piezoelectric/piezomagnetic materials subjected to a uniform tension loading by the generalized Almansi's theorem.…”

Exact solution for elliptical inclusion in magnetoelectroelastic materials

“…There are some pioneering investigations for various crack problems for magnetoelectroelastic fracture. For example, a series of solutions for general cracking mechanics of magnetoelectroelastic solids were obtained in the works of Zhong and Li (2007), Sladek et al (2008), Zhao et al (2006), Hu et al (2007), Gao et al (2003). Magnetoelectroelastic analysis for a penny-shaped crack in a magnetoelectroelastic material was investigated in the work of Feng et al (2007a,b), Tian and Rajapakse (2008) and Zhong and Li (2008a).…”