Uniformly moving screw dislocation in flexoelectric materials

The anti-plane dynamic flexoelectric problem is stated as a dielectric solid that incorporates gradients of electric polarization and flexoelectricity due to strain gradients. It is shown that the coupling of the mechanical with the electrical problem can be condensed in a single mechanical problem that falls within the area of dynamic couple stress elasticity. Moreover, static and steady state dynamic anti-plane problems of flexoelectric or couple stress elastic materials can be modeled as anisotropic plates with a non-equal biaxial pre-stress. This analogy is materialized in a finite element code. Screw dislocations play prominent role in crystal growth, plasticity, development of thin epitaxial films, micro-components and opto-mechanical devices and are important for our modern understanding of seismology. In general, screw dislocations are treated in the context of anti-plane elasticity. In this work we solve the steady-state problem of a screw dislocation in flexoelectric materials, moving with constant velocity. We investigate the influence of various parameters such as the shear wave velocity and two naturally emerging micro-structural and micro-inertia lengths. In the context of flexoelectricity, the two lengths are attributed to the interplay of the elastic and the flexoelectric parameters. We also investigate the connection of the electric boundary conditions with the boundary conditions of the dynamic couple stress elasticity. Furthermore, we investigate the subsonic and the supersonic steady state dislocation motion and find that the Mach cones depend on the micro-structural as well as the micro-inertial lengths. The presented results are important for all crystalline dielectrics such as ceramics, ice and perovskites that exhibit strong flexoelectric effect, often uncoupled from piezoelectricity.