PSI - Issue 80

Akihide Saimoto et al. / Procedia Structural Integrity 80 (2026) 352–367 A. Saimoto et al. / Structural Integrity Procedia 00 (2023) 000–000

367

16

3  j = 1

γ j  b 3 j µ j

B 23 = − 2

(B.15)

r j    b 1 j r j  

d 22   b 3 j  

b 2 j +  d 12 −

3  j = 1 3  j = 1 3  j = 1

s 12 s 22  µ j   

s 12 s 22

B 31 = 2

(B.16)

µ j −

  b 1 j +  b 2 j

B 32 = 2

(B.17)

r j  b 3 j µ j

B 33 = 2

(B.18)

It can be also verified that B i j are all real number not complex.

References

Dai., N., Lei, I. M., Li, Y., Fang, P., Zhong, J., Recent advances in wearable electromechanical sensors–Moving towards machine learning-assisted wearable sensing systems, Nano Energy, Vol.105 (2023), https: // doi.org / 10.1016 / j.nanoen.2022.108041 Sezer, N., Koc, M., A comprehensive review on the state-of-the-art of piezoelectric energy harvesting, nano Energy, Vol. 80 (2021), https: // doi.org / 10.1016 / j.nanoen.2020.105567 Sosa, H., Plane Problems in piezoelectric media with defects, Int. J. Solids Structures, Vol. 28, No. 4, pp.491-505 (1991) Sosa, H., Khutoryansky, N., New developments concerning piezoelectric materials with defects, Int. J. Solids Structures, Vol.33, No.23, pp.3399 3414 (1996) Sosa, H., Castro, M., On concentrated loads at the boundary of a piezoelectric half plate, J. Mech. Phys. Solids, Vol.42, No.7, pp.1105-1122 (1994) Gao C. F., Fan W. X., Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack, Int. J. Solids Structures, Vol.36, pp.2527-2540 (1999) Sung, J.C., Liou, J.Y., Analysis of a crack embedded in a linear elastic half-plane solid, J. Appl. Mech. Trans. ASME 62 (1), pp.78-86 (1995) Yang, P.S., Liou, J.Y., Sung, J.C., Analysis of a crack in a half-plane piezoelectric solid with traction-induction free boundary, Int. J. Solids Structures, Vol.44, No.25, pp.8556-8578 (2007) Liu, J., Wang, B., Du, S., Electro-elastic Green’s functions for a piezoelectric half-space and their application, Appl. Math. Mech., Vol.18 No.11, pp.1037-1043 (1997) Gao, C. F., Fan, W. X., Green functions for the plane problem in a half-infinite piezoelectric medium, Mech. Res. Commun.,Vol.25, No.1, pp.69-74 (1998) Gao, C. F., Noda, N., Green’s function of a half-infinite piezoelectric body: Exact solutions, Acta Mech, Vol.172, No.3-4, pp.169-179 (2004) Shindo, Y., Narita, F., Sosa, H., Electrostatic analysis of piezoelectric ceramics with surface electrodes, Int. J. Eng. Sci., Vol.36, pp.1001-1009 (1998) Ueda, S., Tani, Y., Hatagaki, A., Thermal Stress Intensity Factors for a Normal Crack in a Semi-Infinite Piezoelectric Material, Journal of the Japan Society of Mechanical Engineers, Ser. A., Vol.72-716, pp.513-519 (2006), In Japanese. Khoroshev, K. G., Glushchenko, Yu. A., Plane electroelastic problem for a cracked piezoelectric half-space subject to remote electric field action, Euro. J. Mech., A Solids, Vol.82 (2020) Qin, Q. H,. Advanced Mechanics of Piezoelectricity, Springer (2012) Bardzokas, D. I., Filshtinsky, M. L., Filshtinsky, L. A., Mathematical Methods in Electro-Magneto-Elasticity, Springer (2007)