Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Nonuniform motion of an edge dislocation in an anisotropic solid. I


Authors: Xanthippi Markenscoff and Lu Qun Ni
Journal: Quart. Appl. Math. 41 (1984), 475-494
MSC: Primary 73S05; Secondary 73D99
DOI: https://doi.org/10.1090/qam/724058
MathSciNet review: 724058
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The two-dimensional problem of the nonuniform motion of an edge dislocation in an anisotropic solid (regular hyperbolic case) is solved by means of Laplace transforms with inversion according to the Cagniard-de Hoop technique. The solution is also evaluated asymptotically at the saddle points on the Cagniard-de Hoop contour which lies on a multi-sheet Riemann surface, the singular points of which are examined in detail also in connection to the slowness surface. The stress field is square root singular near the wavefront for a motion of constant velocity starting from rest, and 2/3 singular near the cusp-tips. For general nonuniform motion the stress at the wavefront is obtained as well and an example is given for a motion starting with constant acceleration.


References [Enhancements On Off] (What's this?)

  • [1] A. W. Sáenz, J. Rat. Mech. Anal. 2 (1953), 83
  • [2] R. Bullough and B. A. Bilby, Uniformly moving dislocations in anisotropic media, Proc. Phys. Soc. Sect. B. 67 (1954), 615–624. MR 0063272
  • [3] L. J. Teutonico, Phys. Rev. 124 (1961), 1039
  • [4] J. D. Eshelby, The equation of motion of a dislocation, Phys. Rev. (2) 90 (1953), 248–255. MR 0066922
  • [5] J. Weertman and J. R. Weertman, Dislocations in solids Vol. 3 (edited by F. R. N. Nabarro) North Holland, 1980
  • [6] X. Markenscoff and R. J. Clifton, J. Mech. Phys. Soc. 29 (1981), 253
  • [7] X. Markenscoff and R. J. Clifton, J. Appl. Mech. ASME 49 (1982), 792
  • [8] G. F. D. Duff, The Cauchy problem for elastic waves in an anistropic medium, Philos. Trans. Roy. Soc. London Ser. A 252 (1960), 249–273. MR 0111293, https://doi.org/10.1098/rsta.1960.0006
  • [9] L. J. Teutonico, Mathematical theory of dislocations (edited by T. Mura), ASME, New York, 1969, 49
  • [10] J. D. Eshelby, Phil. Mag. 40 (1949), 903
  • [11] J. D. Eshelby, W. T. Read and W. Shockley, Acta Met 1 (1953), 251
  • [12] J. R. Willis, Phil. Mag., Sec. 8, 21 (1970), 931
  • [13] R. Burridge, The directions in which Rayleigh waves may be propagated on crystals., Quart. J. Mech. Appl. Math. 23 (1970), 217–224. MR 0266479, https://doi.org/10.1093/qjmam/23.2.217
  • [14] A. T. de Hoop, Appl. Sci. Res., B8 (1960), 349
  • [15] R. Burridge, Lamb’s problem for an anisotropic half-space, Quart. J. Mech. Appl. Math. 24 (1971), 81–98. MR 0299059, https://doi.org/10.1093/qjmam/24.1.81
  • [16] E. A. Kraut, Reviews of Geophysics 1 (1963), 401
  • [17] M. J. P. Musgrave, Crystal acoustics, Halden-Day Inc. 1970
  • [18] Xanthippi Markenscoff, The transient motion of a nonuniformly moving dislocation, J. Elasticity 10 (1980), no. 2, 193–201 (English, with French summary). MR 576167, https://doi.org/10.1007/BF00044503
  • [19] Leon Knopoff and Freeman Gilbert, First motion methods in theoretical seismology, J. Acoust. Soc. Amer. 31 (1959), 1161–1168. MR 0108370, https://doi.org/10.1121/1.1907845
  • [20] N. Bleinstein and R. A. Handelman, Asymptotic expansions of integrals, Holt, Reinhart & Winston, New York, 1975
  • [21] W. L. Ferrar, Higher algebra, Oxford University Press, 1948
  • [22] L. B. Freund, Quart. Appl. Math. 30 (1972), 271
  • [23] David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, v. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923
  • [24] L. Sirovich, Techniques of asymptotic analysis, Applied Mathematical Sciences, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0275034
  • [25] X. Markenscoff, Int. J. Engng. Sci. 20 (1982), 289

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73S05, 73D99

Retrieve articles in all journals with MSC: 73S05, 73D99


Additional Information

DOI: https://doi.org/10.1090/qam/724058
Article copyright: © Copyright 1984 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website