The simple asymptotic problem of an impermeable crack in an electrostrictive ceramic under electric loading is analyzed. Closed form solutions of elastic fields are obtained by using the complex function theory. It is found that the K I -dominant region is very small compared to the electric saturation zone. A fracture parameter for an electrostrictive material subjected to electric loading is discussed. In order to investigate the influence of the transverse electric displacement on fracture behavior under the small-scale conditions, we also consider the modified boundary layer problem of a crack in an electrostrictive material. Analytic solutions of electric displacement fields for the asymptotic problem are obtained based on the nonlinear dielectric theory from a modified boundary layer analysis. The shape of the electric displacement saturation zone is shown to depend on the transverse electric displacement. Stress intensity factors induced by the electrostrictive strains are evaluated using the nonlinear solution of the electric displacements. It is found that the transverse electric displacement affects strongly the variation of the mode mixity.

A crack with an electric displacement saturation zone in an electrostrictive material under purely electric loading is analyzed. A strip saturation model is here employed to investigate the effect of the electrical polarization saturation on electric fields and elastic fields. A closed form solution of electric fields and elastic fields for the crack with the strip saturation zone is obtained by using the complex function theory. It is found that the K I -dominant region is very small compared to the strip saturation zone. The generalized Dugdale zone model is also employed in order to investigate the effect of the saturation zone shape on the stress intensity factor. Using the body force analogy, the stress intensity factor for the asymptotic problem of a crack with an elliptical saturation zone is evaluated numerically.

The characterization of the mechanical properties of fuel cell electrodes through the experimental techniques is a complex task due to the low thickness, constituents' heterogeneous composition, and fragile nature of the film. We present a preliminary investigation on the thermomechanical response of fuel cell catalyst layer (CL) obtained through the numerical experiment. Since the Nafion ionomer is one of the constituents' of the CL, a modified micromechanically motivated viscoplastic model is adopted to characterize the Nafion ionomer in terms of reduced density factor to account for the void content. The catalyst agglomerates are taken as inclusions in the ionomer matrix to form a composite unit which is used to plot the true stress–true strain response. Practicality of this work is tested by implementing the electrode layer as a separate component in the single fuel cell unit cell model. A remarkable difference in the magnitude of stress levels in the membrane is observed under thermal and hydrated conditions with the presence and absence of electrode layer in the simulation domain. The present work will assist in improved understanding of the localized stress distribution in the membrane, which is essential to understand its mechanical endurance.

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A thin electrode embedded in an electrostrictive material under electric loading is investigated. In order to obtain an asymptotic form of electric fields and elastic fields near the electrode edge, we consider a modified boundary layer problem of an electrode in an electrostrictive material under the small scale saturation condition. The exact electric solution for the electrode is obtained by using the complex function theory. It is found that the shape of the electric displacement saturation zone is sensitive to the transverse electric displacement. A perturbation solution of stress fields induced by incompatible electrostrictive strains for the small value of the transverse electric displacement is obtained. The influence of transverse electric displacement on a microcrack initiation from the electrode edge is also discussed.