For electro-mechanical impedance (EMI) technique based Structural Health Monitoring (SHM), the piezo ceramic patches are employed with adhesive bond to evaluate and diagnose the host structure to be monitored. The adhesive bond forms a definite layer for force transmission between the patch and host structure. The mechanical and geometrical properties of the adhesive bond layer has significant effect on the overall performance of the PZT-structure interaction. This paper represents the effect geometrical deformation bonding area in the coupled admittance signature through mathematical modelling. The debonding effect has modelled for piezo elasto-dynamic system. In this paper, the mathematical modelling for 1D piezo elastic structure for debonding case and the results are compared with perfect bonding and definite bonding of adhesive bond for PZT-Structure interaction. The paper also studied parametric variation of bond parameter to examine the influence on the EMI based structural signature. © 2019 IEEE.