References
1. Niino, M.H.T. and Watanabe, R. \The functionally
gradient materials", Journal of Japan Society for
Composite Materials, 13, pp. 257-264 (1987).
2. Erdogan, F. \Fracture mechanics of functionally
graded materials", Composites Engineering, 5(7), pp.
753-770 (1995).
3. Jin, Z.H. and Batra, R.C. \Some basic fracture mechanics
concepts in functionally graded materials",
Journal of the Mechanics and Physics of Solids, 44(8),
pp. 1221-1235 (1996).
4. Ming-Che, L. and Erdogan, F. \Stress intensity factors
in two bonded elastic layers containing cracks
perpendicular to and on the interface-I. Analysis",
Engineering Fracture Mechanics, 18(3), pp. 491-506
(1983).
5. Delale, F. and Erdogan, F. \Interface crack in a nonhomogeneous
elastic medium", International Journal
of Engineering Science, 26(6), pp. 559-568 (1988).
6. Erdogan, F. and Wu, B. \Interface crack problems in
layered orthotropic materials", Journal of the Mechanics
and Physics of Solids, 41(5), pp. 889-917 (1993).
7. Erdogan, F., Kaya, A.C., and Joseph, P.F. \The
mode III crack problem in bonded materials with a
nonhomogeneous interfacial zone", Journal of Applied
Mechanics, 58(2), pp. 419-427 (1991).
8. Lu, N.-C., Yang, D.-N., Cheng, Y.-H., and Cheng,
J. \Asymmetrical dynamic propagation problems on
mode III interface crack", Applied Mathematics and
Mechanics, 28(4), pp. 501-510 (2007).
9. Ding, S.-H. and Li, X. \Anti-plane problem of periodic
interface cracks in a functionally graded coatingsubstrate
structure", International Journal of Fracture,
153(1), pp. 53-62 (2008).
10. Chen, Y.-J. and Chue, C.-H. \Mode III crack problems
of two bonded functionally graded strips with
internal cracks", International Journal of Solids and
Structures, 46(2), pp. 331-343 (2009).
11. Chue, C.-H. and Yeh, C.-N. \Mode III fracture problem
of two arbitrarily oriented cracks located within
two bonded functionally graded material strips", Meccanica,
46(2), pp. 447-469 (2010).
12. Wan, Y., Yue, Y., and Zhong, Z. \A mode III crack
crossing the magnetoelectroelastic bimaterial interface
under concentrated magnetoelectromechanical loads",
International Journal of Solids and Structures, 49(21),
pp. 3008-3021 (2012).
13. Chao, C.K. and Lu, L.M. \Mode-III stress intensity
factors of an arbitrarily oriented crack crossing interface
in a layered structure", Journal of Mechanics,
29(04), pp. 643-651 (2013).
2580 R. Sourki et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2570{2581
14. Pan, S.-D., Zhou, Z.-G. and Wu, L.-Z. \Basic solutions
of multiple parallel symmetric mode-III cracks in functionally
graded piezoelectric/piezomagnetic material
plane", Applied Mathematics and Mechanics, 34(10),
pp. 1201-1224 (2013).
15. Ding, S.-H. and Li, X. \The collinear crack problem for
an orthotropic functionally graded coating-substrate
structure", Archive of Applied Mechanics, 84(3), pp.
291-307 (2014).
16. Choi, H.J. \Interfacial fracture analysis of bonded
dissimilar strips with a functionally graded interlayer
under antiplane deformation", Mechanics Research
Communications, 78, Part (B) pp. 93-99 (2016).
17. Ordyan, M.G. and Petrova, V.E.E. \Interaction of
cracks in an elastic two-component material under
anti-plane shear loading", Science Journal of Volgograd
State University. Mathematics. Physics, 3, pp.
53-62 (2016).
18. Rogowski, B. \Exact solution for an anti-plane interface
crack in piezoelectro-magneto-elastic bimaterials",
Archive of Applied Mechanics, 87(4), pp. 593-606
(2017).
19. Lapusta, Y., Onopriienko, O., and Loboda, V. \An
interface crack with partially electrically conductive
crack faces under antiplane mechanical and in-plane
electric loadings", Mechanics Research Communications,
81 pp. 38-43 (2017).
20. Lu, N.-C., Li, X.-G., Cheng, Y.-H., and Cheng,
J. \Asymmetrical dynamic propagation problem on
the edges of mode III interface crack subjected to
superimpose loads", Journal of Mechanics, 29(02), pp.
319-326 (2013).
21. Hu, K., Chen, Z., and Fu, J. \Moving dugdale crack
along the interface of two dissimilar magnetoelectroelastic
materials", Acta Mechanica, 226(6), pp. 2065-
2076 (2015).
22. Monfared, M.M. and Ayatollahi, M. \Cracking in
orthotropic half-plane with a functionally graded coating
under anti-plane loading", Acta Mechanica Solida
Sinica, 28(2), pp. 210-220 (2015).
23. Shin, J.W. and Kim, T.-U. \Transient response of a
mode III interface crack between piezoelectric layer
and functionally graded orthotropic layer", International
Journal of Solids and Structures, 90, pp. 122-
128 (2016).
24. Yang, W.-Y., Zhang, S.-Q., Li, J.-L. and Ma, Y.-L.
\Interface crack problems for mode II of double dissimilar
orthotropic composite materials", Applied Mathematics
and Mechanics, 30(5), pp. 585-594 (2009).
25. Cheng, Z., Gao, D., and Zhong, Z. \Interface crack of
two dissimilar bonded functionally graded strips with
arbitrary distributed properties under plane deformations",
International Journal of Mechanical Sciences,
54(1), pp. 287-293 (2012).
26. Bhattacharya, S., Singh, I.V., Mishra, B.K., and Bui,
T.Q. \Fatigue crack growth simulations of interfacial
cracks in bi-layered FGMs using XFEM", Computational
Mechanics, 52(4), pp. 799-814 (2013).
27. Ding, S.-H., Zhou, Y.-T., and Li, X. \Interface
crack problem in layered orthotropic materials under
thermo-mechanical loading", International Journal of
Solids and Structures, 51(25), pp. 4221-4229 (2014).
28. Fan, M., Yi, D.K., and Xiao, Z.M. \Elastic-plastic
stress investigation for an arc-shaped interface crack
in composite material", International Journal of Mechanical
Sciences, 83 pp. 104-111 (2014).
29. Zhao, W.-B., Zhang, X.-X., Cui, X.-C., and Yang, W.-
Y. \Analysis of stress intensity factor in orthotropic bimaterial
mixed interface crack", Applied Mathematics
and Mechanics, 35(10), pp. 1271-1292 (2014).
30. Bui, T.Q. and Zhang, C. \Extended nite element simulation
of stationary dynamic cracks in piezoelectric
solids under impact loading", Computational Materials
Science, 62 pp. 243-257 (2012).
31. Sharma, K., Bui, T., Zhang, C., and Bhargava,
R. \Analysis of a subinterface crack in piezoelectric
bimaterials with the extended nite element method",
Engineering Fracture Mechanics, 104, pp. 114-139
(2013).
32. Liu, P., Yu, T., Bui, T.Q., and Zhang, C. \Transient
dynamic crack analysis in non-homogeneous functionally
graded piezoelectric materials by the X-FEM",
Computational Materials Science, 69, pp. 542-558
(2013).
33. Liu, P., Yu, T., Bui, T.Q., Zhang, C., Xu, Y.,
and Lim, C.W. \Transient thermal shock fracture
analysis of functionally graded piezoelectric materials
by the extended nite element method", International
Journal of Solids and structures, 51(11), pp. 2167-2182
(2014).
34. Yu, T., Bui, T.Q., Liu, P., Zhang, C., and Hirose,
S. \Interfacial dynamic impermeable cracks analysis
in dissimilar piezoelectric materials under coupled
electromechanical loading with the extended nite
element method", International Journal of Solids and
Structures, 67-68, pp. 205-218 (2015).
35. Bui, T.Q. \Extended isogeometric dynamic and static
fracture analysis for cracks in piezoelectric materials
using NURBS", Computer Methods in Applied Mechanics
and Engineering, 295, pp. 470-509 (2015).
36. Bui, T.Q., Hirose, S., Zhang, C., Rabczuk, T., Wu,
C.-T., Saitoh, T., and Lei, J. \Extended isogeometric
analysis for dynamic fracture in multiphase piezoelectric/
piezomagnetic composites", Mechanics of Materials,
97, pp. 135-163 (2016).
37. Doan, D.H., Bui, T.Q., Duc, N.D., and Fushinobu,
K. \Hybrid phase eld simulation of dynamic crack
propagation in functionally graded glass- lled epoxy",
Composites, Part B: Engineering, 99, pp. 266-276
(2016).
38. Wang, Y. and Waisman, H. \Material-dependent
crack-tip enrichment functions in XFEM for modeling
interfacial cracks in bimaterials", International Journal
for Numerical Methods in Engineering, pp. 1-24
(2017).
R. Sourki et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2570{2581 2581
39. Itou, S. \Stress intensity factors for four interfaceclose
cracks between a nonhomogeneous bonding layer
and one of two dissimilar elastic half-planes", European
Journal of Mechanics-A/Solids, 59, pp. 242-251
(2016).
40. Monfared, M.M., Ayatollahi, M., and Bagheri, R. \Inplane
stress analysis of dissimilar materials with multiple
interface cracks", Applied Mathematical Modelling,
40, (19-20) pp. 8464-8474 (2016).
41. Hills, D.A., Kelly, P.A., Dai, D.N. and Korsunsky,
A.M., Solution of Crack Problems: The Distributed
Dislocation Technique, Kluwer Academic Publishers,
(1996).
42. Erdogan, F., Gupta, G.D. and Cook, T.S. \Numerical
solution of singular integral equations", In: G.C. Sih
(Ed.) Methods of Analysis and Solutions of Crack
Problems: Recent Developments in Fracture Mechanics
Theory and Methods of Solving Crack Problems,
Springer Netherlands, Dordrecht, pp. 368-425 (1973)
)
