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Several horizontal cracks in a piezoelectric half-plane under transient loading

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A piezoelectric half-plane weakened by several horizontal cracks is investigated under anti-plane mechanical and in-plane electrical impacts. The distributed dislocation and integral transform techniques are employed to construct integral equations of the multiple dynamic cracks embedded in the piezoelectric half-plane. At first, the stress and the electric fields in the piezoelectric half-plane are calculated by using pattern. Then, by determining distributed dislocation density on the crack surface, a system of singular integral equations with Cauchy-type singularity is derived. The dynamic field stress intensity factors are determined by using the numerical Laplace inversion and dislocation densities. Finally, several examples are solved and the effects of the geometrical parameters and cracks configuration are graphically obtained upon the dynamic field intensity factors.

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  1. Asadi, E.: Analysis of multiple axisymmetric annular cracks in a piezoelectric medium. Eur. J. Mech. A Solid. 30(6), 844–853 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Quan, W., Wu, N.: A review on structural enhancement and repair using piezoelectric materials and shape memory alloys. Smart. Mater. Struct. 21, 013001 (2012)

    Article  Google Scholar 

  3. Irschik, H.: A review on static and dynamic shape control of structures by piezoelectric actuation. Eng. Struct. 24, 5–11 (2012)

    Article  Google Scholar 

  4. Bagheri, R., Ayatollahi, M., Mousavi, S.M.: Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating. Int. J. Mech. Sci. 93, 93–101 (2015)

    Article  Google Scholar 

  5. Bagheri, R., Ayatollahi, M., Mousavi, S.M.: Analytical solution of multiple moving cracks in functionally graded piezoelectric strip. Appl. Math. Mech. Engl. Ed. 36, 777–792 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  6. Nourazar, M., Ayatollahi, M., Miandari, J., Varasteh, S.: Fracture analysis of a cracked orthotropic strip bonded to a magneto-electro-elastic layer. Proc. Struct. Integr. 2, 3423–3431 (2016)

    Article  Google Scholar 

  7. Chen, Z.T., Karihaloo, B.L.: Dynamic response of a cracked piezoelectric ceramic arbitrary electro-mechanical impact. Int. J. Solids Struct. 36, 5125–5133 (1999)

    Article  MATH  Google Scholar 

  8. Zhu, T., Yang, W.: Crack kinking in a piezoelectric solid. Int. J. Solids Struct. 36, 5013–5027 (1999)

    Article  MATH  Google Scholar 

  9. Xu, X.L., Rajapakse, R.K.N.D.: A theoretical study of branched cracks in piezoelectrics. Acta Mater. 48, 1865–1882 (2000)

    Article  Google Scholar 

  10. Li, X.F.: Transient response of a piezoelectric material with a semi-infinite mode-III crack under impact loads. Int. J. Fract. 111, 119–130 (2001)

    Article  Google Scholar 

  11. Li, X.F., Fan, T.Y.: Transient analysis of a piezoelectric strip with a permeable crack under anti-plane impact loads. Int. J. Eng. Sci. 40, 131–143 (2002)

    Article  Google Scholar 

  12. Zhao, X., Meguid, S.A., Liew, K.M.: The transient response of bonded piezoelectric and elastic half-space with multiple interfacial collinear cracks. Acta. Mech. 159, 11–27 (2002)

    Article  MATH  Google Scholar 

  13. Gu, B., Wang, X., Yu, S.W., Gross, D.: Transient response of Griffith crack between dissimilar piezoelectric layers under anti-plane mechanical and in-plane electrical impacts. Eng. Fract. Mech. 69, 565–576 (2002)

    Article  Google Scholar 

  14. Li, X.F., Tang, G.J.: Transient response of a piezoelectric ceramic strip with an eccentric crack under electromechanical impacts. Int. J. Solids. Struct. 40, 3571–3588 (2003)

    Article  MATH  Google Scholar 

  15. Zhang, Ch., Sladek, J., Sladek, V.: Effects of material gradients on transient dynamic mode-III stress intensity factors in a FGM. Int. J. Solids Struct. 40, 5251–5270 (2003)

    Article  MATH  Google Scholar 

  16. Yong, H.D., Zhou, Y.H.: Transient response of a cracked magnetoelectroelastic strip under anti-plane impact. Int. J. Solids. Struct. 44, 705–717 (2007)

    Article  MATH  Google Scholar 

  17. García-Sánchez, F., Zhang, Ch., Sáez, A.: 2-D transient dynamic analysis of cracked piezoelectric solids by a time-domain BEM. Methods Appl. Mech. Eng. 197, 3108–3121 (2008)

    Article  MATH  Google Scholar 

  18. Chen, X.: Dynamic crack propagation in a magneto-electro-elastic solid subjected to mixed loads: transient Mode-III problem. Int. J. Solids. Struct. 46, 4025–4037 (2009)

    Article  MATH  Google Scholar 

  19. Lei, J., Garcı’a-Sa’nchez, F., Zhang, Ch.: Transient response of an insulating crack near to the interface between two piezoelectric half-planes under electromechanical impacts by BEM. Eng. Anal. Bound. Elem. 36, 1205–1212 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. Bleustein, J.L.: A new surface wave in piezoelectric materials. Appl. Phys. Lett. 13, 412–413 (1968)

    Article  Google Scholar 

  21. Wang, B.L., Mai, Y.W.: Impermeable crack and permeable crack assumptions, which one is more realistic? J. Appl. Mech. Trans. ASME. 71, 575–578 (2004b)

    Article  MATH  Google Scholar 

  22. Weertman, J.: Dislocation Based Fracture Mechanics. World Scientifc, Singapore (1996)

    Book  MATH  Google Scholar 

  23. Korsunsky, A.M., Hills, D.A.: The solution of crack problems by using distributed strain nuclei. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 210, 23–31 (1996)

    Article  Google Scholar 

  24. Cohen, A.M.: Numerical Methods for Laplace Transform Inversion. Springer, Berlin (2007)

    MATH  Google Scholar 

  25. Kuznetsov, A.: On the convergence of the Gaver–Stehfest algorithm. SIAM J. Numer. Anal. 51, 2984–2998 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  26. Erdogan, F., Gupta, G.D., Cook, T.S.: Numerical solution of integral equations. In: Sih, G.C. (ed.) Methods of Analysis and Solution of Crack Problems, pp. 368–425. Noordhoof, Leyden (Holland) (1973)

    Chapter  Google Scholar 

  27. Garcı’a-Sa’nchez, F., Zhang, Ch., Sla’dek, J., Sla’dek, V.: 2D transient dynamic crack analysis in piezoelectric solids by BEM. Comput. Mater. Sci. 39, 179–186 (2007)

    Article  Google Scholar 

  28. Feng, W.J., Li, Y.S., Xu, Z.H.: Transient response of an interfacial crack between dissimilar magnetoelectroelastic layers under magnetoelectromechanical impact loadings: Mode-I problem. Int. J. Solids. Struct. 46, 3346–3356 (2009)

    Article  MATH  Google Scholar 

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Bagheri, R. Several horizontal cracks in a piezoelectric half-plane under transient loading. Arch Appl Mech 87, 1979–1992 (2017).

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