Crack extension force in a dielectric medium

Abstract

The authors' previously derived path-independent integral [1], which is related to the energy-release rate, is evaluated for a crack placed in an infinite dielectric medium subjected to a far field uniaxial tension and an external electric field. The governing equations and boundary conditions for a fully nonlinear elastic dielectric are linearized to a quasi-linear form. Electric field quantities are then decomposed into a rigid body state and a deformed state. This leads to a set of linear differential equations, boundary conditions and constitutive relations. An integral transform technique is used to obtain the solution in closed form. From this solution the crack extension force is evaluated.