Anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable regular triangle nano-hole in magnetoelectroelastic materials

Based on the Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable triangle nano-hole in magnetoelectroelastic materials with surface effect is studied. The exact solutions of the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate are obtained under the boundary conditions of magnetoelectrically permeable and impermeable. The numerical examples show the influence of surface effect on the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate under two different boundary conditions. It can be seen that the surface effect leads to the coupling of stress, electric and magnetic field, and with the increase of cavity size, the influence of surface effect begins to decrease until it tends to classical elasticity theory.

On Discovery of the Twelfth and Thirteenth New Nondispersive SH-SAWs in 6 mm Magnetoelectroelastics

This report acquaints the reader with an extra two new shear-horizontal surface acoustic waves (SH-SAWs). These new SH-SAWs can propagate along the free surface of the transversely isotropic (6 mm) magnetoelectroelastic materials. These (composite) materials can simultaneously possess the piezoelectric, piezomagnetic, and magnetoelectric effects. Some competition among these effects can lead to suitable solutions found for the following three possible coupling mechanisms: eα – hε, eµ – hα, εµ – α2. Here, the mechanically free interface between the solid and a vacuum was considered. This report discovers the twelfth (thirteenth) new SH-SAW for the magnetically closed (electrically open) case and continuity of both the normal component of the electrical (magnetic) displacement and the electrical (magnetic) potential when the coupling mechanism eα – hε (eµ – hα) works. The propagation velocities were obtained in explicit forms that take into account the contribution of the vacuum material parameters. The discovered waves were then graphically studied for the purpose of disclosing the dissipation phenomenon (the propagation velocity becomes imaginary) caused by the coupling with the vacuum properties. The obtained results can be useful for further investigations of interfacial and plate SH-waves, constitution of technical devices, nondestructive testing and evaluation, and application of some gravitational phenomena.