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Moving row of antiplane shear cracks within one-dimensional piezoelectric quasicrystals

  • Received: 18 August 2016 Accepted: 08 October 2016 Published: 14 October 2016
  • Closed-form expressions are deduced and discussed, using an extended form of the classical dislocation layer method, for the phonon and phason stress and electric displacement components and intensity factors generated in one-dimensional piezoelectric quasicrystals by a collinear row of moving shear cracks. Representative numerical results are presented graphically. Additionally, this analysis yields the fields of a single crack moving in a finite piezoelectric quasicrystalline plate and also of a moving edge crack in a plate

    Citation: Geoffrey E. Tupholme. Moving row of antiplane shear cracks within one-dimensional piezoelectric quasicrystals[J]. AIMS Materials Science, 2016, 3(4): 1365-1381. doi: 10.3934/matersci.2016.4.1365

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  • Closed-form expressions are deduced and discussed, using an extended form of the classical dislocation layer method, for the phonon and phason stress and electric displacement components and intensity factors generated in one-dimensional piezoelectric quasicrystals by a collinear row of moving shear cracks. Representative numerical results are presented graphically. Additionally, this analysis yields the fields of a single crack moving in a finite piezoelectric quasicrystalline plate and also of a moving edge crack in a plate


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    [1] Shechtman D, Blech I, Gratias D, et al. (1984) Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53: 1951–1953. doi: 10.1103/PhysRevLett.53.1951
    [2] Fan TY (2011) The mathematical theory of elasticity of quasicrystals and its applications. Science Press, Springer-Verlag, Beijing/Heidelberg.
    [3] Fan TY (2013) Mathematical theory and methods of mechanics of quasicrystalline materials. Engineering 5: 407–448. doi: 10.4236/eng.2013.54053
    [4] Ding DH, Yang WG, Hu CZ, et al. (1993) Generalized elasticity theory of quasicrystals. Phys Rev B 48: 7003–7009. doi: 10.1103/PhysRevB.48.7003
    [5] Altay G, Dökmeci MC (2012) On the fundamental equations of piezoelasticity of quasicrystal media. Int J Solids Struct 49: 3255–3262. doi: 10.1016/j.ijsolstr.2012.06.016
    [6] Li CL, Liu YY (2004) The physical property tensors of one-dimensional quasicrystals. Chin Phys 13: 924–931. doi: 10.1088/1009-1963/13/6/024
    [7] Wang X, Pan E (2008) Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals. Pramana J Phys 70: 911–933. doi: 10.1007/s12043-008-0099-8
    [8] Yang LZ, Gao Y, Pan E, et al. (2014) Electric-elastic field induced by a straight dislocation in one-dimensional quasicrystals. Acta Phys Polonica A 126: 467–470. doi: 10.12693/APhysPolA.126.467
    [9] Li XY, Li PD, Wu TH, et al. (2014) Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys Lett A 378: 826–834. doi: 10.1016/j.physleta.2014.01.016
    [10] Yu J, Guo J, Xing Y (2015) Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals. Chin J Aero 28: 1287–1295. doi: 10.1016/j.cja.2015.04.013
    [11] Yu J, Guo J, Pan E, et al. (2015) General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics. Appl Math Mech 36: 793–814. doi: 10.1007/s10483-015-1949-6
    [12] Zhang L, Zhang Y, Gao Y (2014) General solutions of plane elasticity of one-dimensional orthorhombic quasicrystals with piezoelectric effect. Phys Lett A 378: 2768–2776. doi: 10.1016/j.physleta.2014.07.027
    [13] Yang J, Li X (2016) Analytical solutions of problem about a circular hole with a straight crack in one-dimensional hexagonal quasicrystals with piezoelectric effects. Theor Appl Fract Mech 82: 17–24. doi: 10.1016/j.tafmec.2015.07.012
    [14] Guo J, Zhang Z, Xing Y (2016) Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites. Phil Mag 96: 349–369. doi: 10.1080/14786435.2015.1132852
    [15] Fan C, Li Y, Xu G, et al. (2016) Fundamental solutions and analysis of three-dimensional cracks in one-dimensional hexagonal piezoelectric quasicrystals. Mech Res Comm 74: 39–44. doi: 10.1016/j.mechrescom.2016.03.009
    [16] Tupholme GE, One-dimensional piezoelectric quasicrystals with an embedded moving, non-uniformly loaded shear crack. Acta Mech [in press].
    [17] Guo J, Pan E (2016) Three-phase cylinder model of one-dimensional piezoelectric quasi-crystal composites. ASME J Appl Mech 83: 081007. doi: 10.1115/1.4033649
    [18] Guo J, Yu J, Xing Y, et al. (2016) Thermoelastic analysis of a two-dimensional decagonal quasicrystal with a conductive elliptic hole. Acta Mech 227: 2595–2607. doi: 10.1007/s00707-016-1657-7
    [19] Bilby BA, Eshelby JD (1968) Dislocations and the theory of fracture. In: Liebowitz H, Fracture, New York: Academic Press, 1: 99–182.
    [20] Lardner RW (1974) Mathematical theory of dislocations and fracture. University of Toronto Press, Toronto.
    [21] Leibfried G (1951) Verteilung von versetzungen im statischen gleichgewicht. Z Phys 130: 214–226. doi: 10.1007/BF01337695
    [22] Muskhelishvili NI (1953) Singular integral equations. Noordhoff Int. Pub., Leyden.
    [23] Gakhov FD (1966) Boundary value problems. Pergamon, Oxford.
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