A singular asymptotic expansion for the field near a moving dislocation loop
Authors:
Constantine Callias, Xanthippi Markenscoff and Lu Qun Ni
Journal:
Quart. Appl. Math. 48 (1990), 113-132
MSC:
Primary 73S10
DOI:
https://doi.org/10.1090/qam/1040237
MathSciNet review:
MR1040237
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The coefficients of the $1/\varepsilon$ and ln $\varepsilon$ singular terms in the field quantities near an arbitrarily moving dislocation loop are obtained by singular asymptotic expansion of integrals.
J. D. Achenbach, Wave Propagation in Elastic Solids, North Holland, Amsterdam-London, 1973
R. Burridge and L. Knopoff, Body-force equivalent for seismic dislocations, Bull. Seismol. Soc. Amer. 54, 1854–1888 (1962)
- C. Callias and X. Markenscoff, Singular asymptotics of integrals and the near-field radiated from nonuniformly moving dislocations, Arch. Rational Mech. Anal. 102 (1988), no. 3, 273–285. MR 944549, DOI https://doi.org/10.1007/BF00281350
R. J. Clifton and X. Markenscoff, Elastic precursor decay and radiation from nonuniformly moving dislocations, J. Mech. Phys. Solids 29, 227–251 (1981)
J. D. Eshelby, Uniformly moving dislocations, Proc. Phys. Soc. A62, 307–314 (1949)
- J. D. Eshelby, The equation of motion of a dislocation, Phys. Rev. (2) 90 (1953), 248–255. MR 66922
F. C. Frank, On the equation of motion of crystal dislocations, Proc. Phys. Soc. 62A, 131–134 (1949)
H. Günther, Uberschallbewegung von Eigenspannungsguellen in der Kontinuumstheorie, Annalen der Physik 21, 93–105 (1968)
J. Kuisalaas and T. Mura, On the motion of a screw dislocation, Recent Advances in Engng. Sci. (A. C. Eringen, ed.), Gordon and Breach, New York, 1964, pp. 543–563
J. Kuisalaas and T. Mura, On the elastic field around an edge dislocation with application to dislocation vibration, Phil. Mag. 9, 1–7 (1964)
R. Madariaga, Dynamics of an expanding circular fault, Bull. Seismol. Soc. Amer. 66, 639–666 (1976)
- Xanthippi Markenscoff, The transient motion of a nonuniformly moving dislocation, J. Elasticity 10 (1980), no. 2, 193–201 (English, with French summary). MR 576167, DOI https://doi.org/10.1007/BF00044503
X. Markenscoff and R. J. Clifton, The nonuniformly moving edge dislocation, J. Mech. Phys. Solids 29, 253–262 (1981)
X. Markenscoff and R. J. Clifton, Radiation from expanding circular dislocation loops and elastic precursor decay, J. Appl. Mech. ASME 49, 792–796 (1982)
- Xanthippi Markenscoff and Lu Qun Ni, Nonuniform motion of an edge dislocation in an anisotropic solid. I, Quart. Appl. Math. 41 (1983/84), no. 4, 475–494. MR 724058, DOI https://doi.org/10.1090/S0033-569X-1984-0724058-1
X. Markenscoff, On the effect of dislocation loop curvature on elastic precursor decay, J. Appl. Mech. ASME 51, 753–758 (1984)
- Xanthippi Markenscoff and Lu Qun Ni, The singular nature of the stress field near an arbitrarily moving dislocation loop, J. Mech. Phys. Solids 38 (1990), no. 4, 481–490. MR 1060204, DOI https://doi.org/10.1016/0022-5096%2890%2990009-S
T. Mura, Continuous distributions of moving dislocations, Phil. Mag 8, 843–856 (1963)
T. Mura, Methods of continuously distributed dislocations, Mathematical Theory of Dislocations (ASME) (T. Mura, ed.), 1969, pp. 25–48
J. D. Achenbach, Wave Propagation in Elastic Solids, North Holland, Amsterdam-London, 1973
R. Burridge and L. Knopoff, Body-force equivalent for seismic dislocations, Bull. Seismol. Soc. Amer. 54, 1854–1888 (1962)
C. Callias and X. Markenscoff, Singular asymptotics of integrals and the near-field of a nonuniformly moving dislocation, Arch. Rational Mech. Anal. 102, 73–205 (1988)
R. J. Clifton and X. Markenscoff, Elastic precursor decay and radiation from nonuniformly moving dislocations, J. Mech. Phys. Solids 29, 227–251 (1981)
J. D. Eshelby, Uniformly moving dislocations, Proc. Phys. Soc. A62, 307–314 (1949)
J. D. Eshelby, The Equation of motion of a dislocation, Phys. Rev. 90, 248–255 (1953)
F. C. Frank, On the equation of motion of crystal dislocations, Proc. Phys. Soc. 62A, 131–134 (1949)
H. Günther, Uberschallbewegung von Eigenspannungsguellen in der Kontinuumstheorie, Annalen der Physik 21, 93–105 (1968)
J. Kuisalaas and T. Mura, On the motion of a screw dislocation, Recent Advances in Engng. Sci. (A. C. Eringen, ed.), Gordon and Breach, New York, 1964, pp. 543–563
J. Kuisalaas and T. Mura, On the elastic field around an edge dislocation with application to dislocation vibration, Phil. Mag. 9, 1–7 (1964)
R. Madariaga, Dynamics of an expanding circular fault, Bull. Seismol. Soc. Amer. 66, 639–666 (1976)
X. Markenscoff, The transient motion of a nonuniformly moving dislocation, J. of Elasticity 10, 193–201 (1980)
X. Markenscoff and R. J. Clifton, The nonuniformly moving edge dislocation, J. Mech. Phys. Solids 29, 253–262 (1981)
X. Markenscoff and R. J. Clifton, Radiation from expanding circular dislocation loops and elastic precursor decay, J. Appl. Mech. ASME 49, 792–796 (1982)
X. Markenscoff and L. Ni, Nonuniform motion of an edge dislocation in an anisotropic solid, Quart. Appl. Math. 41, 475–494 (1984)
X. Markenscoff, On the effect of dislocation loop curvature on elastic precursor decay, J. Appl. Mech. ASME 51, 753–758 (1984)
X. Markenscoff and L. Ni, The singular nature of the stress field near an arbitrarily moving dislocation loop, J. Mech. Phys. Solids., (to appear in 1989)
T. Mura, Continuous distributions of moving dislocations, Phil. Mag 8, 843–856 (1963)
T. Mura, Methods of continuously distributed dislocations, Mathematical Theory of Dislocations (ASME) (T. Mura, ed.), 1969, pp. 25–48
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73S10
Retrieve articles in all journals
with MSC:
73S10
Additional Information
Article copyright:
© Copyright 1990
American Mathematical Society
