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: 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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G. C. Sih, Some elastodynamic problems of cracks, Internat. J. Fracture 4, 51–68 (1968)
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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)
F. Nilsson, Dynamic stress intensity factor for finite strip problems, Internat. J. Fracture 8, 403–411 (1972)
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M. K. Kassir and S. Tse, Moving Griffith crack in an orthotropic material, Internat. J. Engrg. Sci. 21, 315–325 (1983)
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)
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E. H. Yoffè, The moving Griffith crack, Philos. Mag. 42, 739–750 (1951)
J. R. M. Radok, On the solution of problems of dynamic plane elasticity, Quart. Appl. Math. 14, 289–298 (1956)
J. W. Craggs, On the propagation of a crack in an elastic brittle material, J. Mech. Phys. Solids 8, 66–75 (1960)
F. A. McClintock and S. P. Sukhatme, Travelling cracks in elastic materials under longitudinal shear, J. Mech. Phys. Solids 8, 187–193 (1960)
G. C. Sih, Some elastodynamic problems of cracks, Internat. J. Fracture 4, 51–68 (1968)
G. C. Sih and E. P. Chen, Moving cracks in a finite strip under tearing action, J. Franklin Inst. 290, 25–35 (1970)
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)
F. Nilsson, Dynamic stress intensity factor for finite strip problems, Internat. J. Fracture 8, 403–411 (1972)
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)
R. J. Tait and T. B. Moodie, On a problem in the dynamic theory of cracks, Quart. Appl. Math. 38, 419–423 (1981)
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)
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)
C. Atkinson, The propagation of fracture in aelotropic materials, Internat. J. Fracture Mechanics 1, 47–55 (1965)
M. K. Kassir and S. Tse, Moving Griffith crack in an orthotropic material, Internat. J. Engrg. Sci. 21, 315–325 (1983)
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)
A. Piva, Elastodynamic crack problems in an anisotropic medium through a complex variable approach, Quart. Appl. Math. 44, 441–445 (1986)
S. G. Lekhnitskii, Theory of elasticity of an anisotropic elastic body, Holden-Day (1963)
F. D. Gakhov, Boundary value problems, Pergamon Press (1966)
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Article copyright:
© Copyright 1987
American Mathematical Society