Transient dynamic Green’s functions for a cracked plane
Author:
L. M. Brock
Journal:
Quart. Appl. Math. 44 (1986), 265-275
MSC:
Primary 73M05
DOI:
https://doi.org/10.1090/qam/856180
MathSciNet review:
856180
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Abstract: Closed-form solutions for the transient dynamic problems of a suddenly applied anti-plane concentrated force and concentrated impulse near a crack are obtained. The various wave signals comprising the solutions are identified, and their behavior noted. The concentrated force solution is then employed as a Green’s function to solve the important problem of arbitrary screw dislocation motion near a crack edge.
J. W. Rudnicki, “Fracture mechanics applied to the earth’s crust,” in Annual Review of Earth Planetary Science, pp. 489–525 (1980)
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J. D. Achenbach, A. K. Gautesen, and H. McMaken, “Diffraction of elastic waves by cracks-analytical results,” in Elastic Waves and Non-destructive Testing of Materials, AMD-Vol. 29 (Pao, Y. H., ed.) ASME, New York (1978)
- L. M. Brock, The dynamic $2$D analysis of a concentrated force near a semi-infinite crack, Quart. Appl. Math. 43 (1985), no. 2, 201–210. MR 793528, DOI https://doi.org/10.1090/S0033-569X-1985-0793528-2
L. M. Brock, The dynamic stress intensity factor due to arbitrary screw dislocation motion, J. Appl. Mech. 50 383–389 (1983)
I. N. Sneddon, The use of integral transforms, McGraw-Hill, New York (1972)
- George F. Carrier and Carl E. Pearson, Partial differential equations, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Theory and technique. MR 0404823
B. V. Kostrov, Unsteady propagation of longitudinal shear cracks, Prikladnaya Matemi Mekhanika 30 (English translation), 1241–1248 (1966)
J. D. Achenbach, Extension of a crack by a shear wave, Zeitschrift für angewandte Mathematik und Physik 21, 887–900 (1970)
B. O. Pierce and R. M. Foster, A short table of integrals (4th ed.), Ginn and Blaisdell, Waltham, MA (1957)
B. A. Bilby and J. D. Eshelby, Dislocations and the theory of fracture, in Fracture, Vol. 1, Chapter 2 (H. Liebowitz, ed.) Academic Press, New York (1968)
R. Burridge and L. Knopoff, Body force equivalents for seismic dislocations, Bulletin of the Seismological Society of America 54, 1875–1888 (1964)
L. M. Brock, The dynamic stress intensity factor for a crack due to arbitrary rectilinear screw dislocation motion, Journal of Elasticity 13, 429–439 (1983)
J. W. Rudnicki, “Fracture mechanics applied to the earth’s crust,” in Annual Review of Earth Planetary Science, pp. 489–525 (1980)
J. D. Achenbach, A. K. Gautesen, and H. McMaken, Ray methods for elastic waves in solids—with applications to scattering by cracks, Pitman, London (1982)
J. D. Achenbach, A. K. Gautesen, and H. McMaken, “Diffraction of elastic waves by cracks-analytical results,” in Elastic Waves and Non-destructive Testing of Materials, AMD-Vol. 29 (Pao, Y. H., ed.) ASME, New York (1978)
L. M. Brock, The dynamic 2 D analysis of a concentrated force near a semi-infinite crack, Quart. Appl. Math. 43, 201–210 (1985)
L. M. Brock, The dynamic stress intensity factor due to arbitrary screw dislocation motion, J. Appl. Mech. 50 383–389 (1983)
I. N. Sneddon, The use of integral transforms, McGraw-Hill, New York (1972)
G. F. Carrier and C. E. Pearson, Partial differential equations, Academic Press, New York (1976)
B. V. Kostrov, Unsteady propagation of longitudinal shear cracks, Prikladnaya Matemi Mekhanika 30 (English translation), 1241–1248 (1966)
J. D. Achenbach, Extension of a crack by a shear wave, Zeitschrift für angewandte Mathematik und Physik 21, 887–900 (1970)
B. O. Pierce and R. M. Foster, A short table of integrals (4th ed.), Ginn and Blaisdell, Waltham, MA (1957)
B. A. Bilby and J. D. Eshelby, Dislocations and the theory of fracture, in Fracture, Vol. 1, Chapter 2 (H. Liebowitz, ed.) Academic Press, New York (1968)
R. Burridge and L. Knopoff, Body force equivalents for seismic dislocations, Bulletin of the Seismological Society of America 54, 1875–1888 (1964)
L. M. Brock, The dynamic stress intensity factor for a crack due to arbitrary rectilinear screw dislocation motion, Journal of Elasticity 13, 429–439 (1983)
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Article copyright:
© Copyright 1986
American Mathematical Society
