Abstract
A thin electrode embedded in an electrostrictive material under electric loading is investigated. In order to obtain an asymptotic form of electric fields and elastic fields near the electrode edge, we consider a modified boundary layer problem of an electrode in an electrostrictive material under the small scale saturation condition. The exact electric solution for the electrode is obtained by using the complex function theory. It is found that the shape of the electric displacement saturation zone is sensitive to the transverse electric displacement. A perturbation solution of stress fields induced by incompatible electrostrictive strains for the small value of the transverse electric displacement is obtained. The influence of transverse electric displacement on a microcrack initiation from the electrode edge is also discussed.
Similar content being viewed by others
References
Uchino K. (1986). Electrostrictive actuators: materials and applications. Am. Ceram. Soc. Bull. 65: 647–652
Winzer S.R., Shankar N., Ritter A.P. (1989). Designing cofired multilayer electrostrictive actuators for reliability. J. Am. Ceram. Soc. 72: 2246–2257
Aburatani H., Harada S., Uchino K., Furuta A. (1994). Destruction mechanism of ceramic multilayer actuator. Jpn. J. Appl. Phys. 33: 3091–3094
Yang W., Suo Z. (1994). Cracking in ceramic actuators caused by electrostriction. J. Mech. Phys. Solids 42: 649–663
Hao T.H., Gong X., Suo Z. (1996). Fracture mechanics for the design of ceramic multilayer actuators. J. Mech. Phys. Solids 44: 23–48
Gong X., Suo Z. (1996). Reliability of ceramic multiplayer actuators: a Nonlinear finite element simulation. J. Mech. Phys. Solids 44: 751–769
Ru C.Q., Mao X., Epstein M. (1998). Electric-field induced interfacial cracking in multilayer electrostrictive actuators. J. Mech. Phys. Solids 46: 1301–1318
Beom H.G. (1999). Small scale nonlinear analysis of electostrictive crack problem. J. Mech. Phys. Solids 47: 1379–1395
Beom H.G. (1999). Singular behavior near a crack tip in an electrostrictive material. J. Mech. Phys. Solids 47: 1027–1049
Beom H.G. (2001). Effect of polarization saturation on the stress intensity factor for a crack in an electrostrictive ceramic. Philos. Mag. A 81: 2203–2314
Beom H.G., Kim Y.H., Cho C., Kim C.B. (2006). A crack with an electric displacement saturation zone in an electrostrictive material. Arch. Appl. Mech. 76: 19–31
Beom H.G., Kim Y.H., Cho C., Kim C.B. (2006). Asymptotic analysis of an impermeable crack in an electrostrictive material subjected to electric loading. Int. J. Solids Struct. 43: 6869–6886
Hult, J.A.H., McClintock, F.A.: Elastic-plastic stress and strain distributions around sharp notches under repeated shear. In: Proceedings of the 9th International Congress for Applied Mechanics, vol. 8, pp. 51–58 (1957)
Rice J.R. (1967). Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear. J. Appl. Mech. 34: 287–298
Dugdale D.S. (1960). Yielding of sheets containing slits. J. Mech. Phys. Solids 8: 100–104
Unger D.J. (1989). A finite-width Dugdale zone model for mode III. Eng. Fract. Mech. 34: 977–987
Turska E., Wisniewski E. (2003). On semi-infinite crack problems in elastic-plastic bodies; uniqueness and examples. Int. J. Eng. Sci. 41: 1767–1783
Knops R.J. (1963). Two-dimensional electrostriction. Q. J. Mech. Appl. Math. 16: 377–388
Tada H., Paris P.C., Irwin G.R. (1985). The Stress Analysis of Cracks Handbook. Del Research, St. Louis, MO
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beom, H.G., Kim, Y.H., Kim, C.B. et al. Modified boundary layer analysis of an electrode in an electrostrictive material. Arch Appl Mech 78, 191–209 (2008). https://doi.org/10.1007/s00419-007-0151-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-007-0151-z