Investigation of the M -integral in crack-damaged piezoelectric ceramics

The physical interpretation of the M-integral is investigated in the analysis of crack-damaged piezoelectric problems. The relation between the M-integral and the change of the total electric enthalpy (CTEE), i.e., M = 2CTEE, is derived with a theoretical derivation procedure for two-dimensional piezoelectric problems. It is shown that the M-integral may provide a more natural description of electric enthalpy release due to the formation of the pre-existing microcracks associated with the damaged body, rather than the description of the total potential energy release rate as interpreted for conventional brittle solids. For crack-damaged piezoelectric ceramics, numerical calculation of the M-integral is discussed. Based on the pseudo-traction electric displacement method, M = 2CTEE has also been proved by the numerical results.