Singular behaviour near a crack tip in an electrostrictive material

A crack in a nonlinear electrostrictive material under electric loading is analyzed. Asymptotic singular solutions in the vicinity of the tip of the c rack with electrically conducting or impermeable surfaces are obtained to t he second order with the help of conservation integrals. The relation betwe en the J-integral and the intensity factors of the stress and the electric field is derived for the conducting crack as well as for the insulating cra ck. Singular solutions near the end of a sheet with a vanishingly small thi ckness in the electrostrictive medium are also obtained. It is verified tha t the stress intensity factor for the crack in the electrostrictive materia l under electric loading has a positive value and the crack surfaces near t he crack tip are open. (C) 1999 Elsevier Science Ltd. All rights reserved.