Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



An alternative approach to elastodynamic crack problems in an orthotropic medium

Author: A. Piva
Journal: Quart. Appl. Math. 45 (1987), 97-104
MSC: Primary 73M05; Secondary 73C30
DOI: https://doi.org/10.1090/qam/885172
MathSciNet review: 885172
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Abstract | References | Similar Articles | Additional Information

Abstract: A similarity transformation is used to reduce the system of second-order equations, governing elastodynamic plane problems in an orthotropic medium, to a first-order elliptic system of the Cauchy-Riemann type. A complex variable notation is then introduced to derive in a straightforward way the solution of two noticeable elastodynamic crack problems.

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  • [1] E. H. Yoffè, The moving Griffith crack, Philos. Mag. 42, 739-750 (1951) MR 0043696
  • [2] J. R. M. Radok, On the solution of problems of dynamic plane elasticity, Quart. Appl. Math. 14, 289-298 (1956) MR 0081075
  • [3] J. W. Craggs, On the propagation of a crack in an elastic brittle material, J. Mech. Phys. Solids 8, 66-75 (1960) MR 0116626
  • [4] F. A. McClintock and S. P. Sukhatme, Travelling cracks in elastic materials under longitudinal shear, J. Mech. Phys. Solids 8, 187-193 (1960) MR 0115408
  • [5] G. C. Sih, Some elastodynamic problems of cracks, Internat. J. Fracture 4, 51-68 (1968)
  • [6] G. C. Sih and E. P. Chen, Moving cracks in a finite strip under tearing action, J. Franklin Inst. 290, 25-35 (1970)
  • [7] G. C. Sih and E. P. Chen, Crack propagation in a strip of material under plane extension, Internat. J. Engrg. Sci. 10, 537-551 (1972)
  • [8] F. Nilsson, Dynamic stress intensity factor for finite strip problems, Internat. J. Fracture 8, 403-411 (1972)
  • [9] R. J. Tait and T. B. Moodie, Complex variable methods and closed-form solutions to dynamic crack and punch problems in the classical theory of elasticity, Internat. J. Engrg. Sci. 19, 221-229 (1981) MR 660549
  • [10] R. J. Tait and T. B. Moodie, On a problem in the dynamic theory of cracks, Quart. Appl. Math. 38, 419-423 (1981) MR 636245
  • [11] B. M. Singh, T. B. Moodie, and J. Haddow, Closed-form solutions for finite length crack moving in a strip under antiplane shear stress, Acta Mech. 38, 99-109 (1981) MR 602014
  • [12] H. G. Georgiadis and P. S. Theocaris, On the solution of steady-state elastodynamic crack problems by using complex variable methods, Z. Angew. Math. Phys. 36, 146-165 (1985) MR 785929
  • [13] C. Atkinson, The propagation of fracture in aelotropic materials, Internat. J. Fracture Mechanics 1, 47-55 (1965) MR 0468447
  • [14] M. K. Kassir and S. Tse, Moving Griffith crack in an orthotropic material, Internat. J. Engrg. Sci. 21, 315-325 (1983)
  • [15] H. T. Danyluk and B. M. Singh, Closed form solutions for a finite length crack moving in an orthotropic layer of finite thickness, Letters Appl. Engrg. Sci. 22, 637-644 (1984)
  • [16] A. Piva, Elastodynamic crack problems in an anisotropic medium through a complex variable approach, Quart. Appl. Math. 44, 441-445 (1986) MR 860897
  • [17] S. G. Lekhnitskii, Theory of elasticity of an anisotropic elastic body, Holden-Day (1963) MR 0180018
  • [18] F. D. Gakhov, Boundary value problems, Pergamon Press (1966) MR 0198152

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DOI: https://doi.org/10.1090/qam/885172
Article copyright: © Copyright 1987 American Mathematical Society

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