MAXWELL STRESS AND ELECTROSTRICTION IN DIELECTRICS AND THEIR IMPLICATIONS FOR FRACTURE MECHANICS

In fracture mechanics of smart materials, the influence of electric fields on the propagation of cracks plays a key role. While the piezoelectric effect has been thoroughly investigated in this regard, nonlinear electrodynamic phenomena are oftentimes
disregarded.
As an example, stemming from the microscopic Lorentz force, electrostatic actions manifest themselves macroscopically in terms of surface tractions at discontinuities, body forces caused by graded fields and body couples due to local non-collinearity of electric field and polarization. All three of these manifestations are derived from the Maxwell stress tensor, whose formulation in polarizable matter is still being debated to date [1]. By contrast, electrostriction represents a constitutive effect only inherent to dielectric materials, interlinking mechanical strains with the square of the electric field and polarization, respectively. Due to identical mathematical structures of electrostrictive and Maxwell stresses in isotropic materials, both effects are sometimes treated equivalently.
In this work, these nonlinearities are studied with respect to an elliptic cavity in an infinite dielectric, providing a Griffith crack in the limiting case of a vanishing semi-minor axis. In this context, predominant models of the Maxwell stress tensor are compared and precisely distinguished from electrostriction, ultimately evaluating their individual contributions to crack tip loading.
EXTENDED ABSTRACT