Mathematical modeling of electro‐elastic dislocations in piezoelectric materials

In this work, based on the theory of linear incompatible piezoelectricity with eigendistortion and eigenelectric field, the concept of electro-elastic dislocations is presented. Both field variables, the displacement vector u and the electrostatic potential φ, possess a jump discontinuity at the dislocation surface. Electro-elastic dislocations are described not only by the dislocation density tensor but also by a new introduced field, the so-called electric dislocation density vector. In addition to electro-elastic dislocations, inhomogeneities, body forces and body charges are also considered. Within this framework, material balance laws that correspond to the symmetries of translation, scaling and rotation are derived. All fundamental fields of configurational mechanics like the Eshelby stress tensor, the electro-elastic Peach-Koehler force, the Cherepanov force, the Eshelby force among others, which take place in the broken (translational, scaling and rotational) conservation laws anymore are given.