A C o m p le x V a ria b le S o lu tio n B ased A n a ly s is of E le c tric D is p la c e m e n t S a tu ra tio n fo r a C racked P ie z o e le c tric M a te ria lThis paper presents an analysis of the effect of electric displacement saturation for a fail ing piezoelectric ceramic material based on a complex variable solution of a Mode III and a Mode I crack. This particular electric nonlinearity is caused by a reduction of the ionic movement in the material in the presence of high electric fields. Total and strain energy release rates are computed for varying far field stresses, electric displacements, and electric fields and compared for cases without and with full electric displacement saturation to further advance the understanding of failure initiation in piezoelectric ceramics.
Basic Equations of Linear PiezoelectricityWithin the small strain range, the primary unknowns of a piezo electric solid 08, which occupies a configuration B C R , are the mechanical displacement field m,-: B -* R 3 and the electric potential R 3xm 3 given aswith R 3x^ representing the space of symmetric tensors, and the electric field e, : B -> R 3 defined by e, = -q>,iHere, (•) , • = d(-)/dxj is the standard gradient operation with respect to the coordinate x,. For the quasi-static case considered
Journal of Applied Mechanics