Thepresentinvestigationofthecrackprobleminpiezoelectricmaterialsisperformedbasedonthenon-localtheory.Aftersomemanipulations,theimpermeablecrack,thepermeablecrack(thecrackgapisfullofNaCIsolution),andthesemi-permeablecrack(thecrackgapisfullofairorsiliconoil)arereducedtoauniformformulationbyassum-ingthenormalelectricdisplacementonthecracksurfacestobeanunknownvariable.Thus,atripleintegralequationwiththeunknownnormalelectricdisplacementisestablished.ByusingtheNewtoniterativemethodandsolvingthetripleinte-gralequation,itisfoundthatthenormalelectricdisplacementonthecracksurfacesisnolongeraconstantasdeterminedbypreviousstudies,rather,itdependsupontheremotecom-binedelectromechanicalloadings.Numericalresultsofthestressesandelectricdisplacementfieldsshowthattherearenosingularitiesatthecracktipssothatthestressesremainfinite.Itisofgreatsignificancethattheconcreteelectricboundaryconditiononthecracksurfacesexertssignificantinfluenceonthenear-tipfieldsandinthiswayplaysanimpor-tantroleinevaluatingthecrackstabilityinthenon-localpiezoelectricmaterials.Morespecifically,theimpermeablecrackmodelalwaysoverestimatesthefinitestressesatthecracktips,whereasthepermeablecrackmodelalwaysunder-estimatesthem.
