# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 2000 Seminar Series**

*Radiating and Non-radiating Dislocations in Uniform Motion in
Anisotropic Elastic Solids*

*Abstract*

### Over 50 years ago the late J. D. Eshelby showed that in an isotropic linear
elastic medium a straight edge dislocation could undergo uniform motion at a
speed equal to times the shear wave speed without radiating energy in its
far-field, i.e., in supersonic motion the dislocation essentially displayed the
character associated with purely subsonic motion. Recently, Rosakis, et al, [1]
have experimentally observed supersonic crack motion at speeds near this
"non-radiating" speed, and Gao, et al, [2] have shown that
non-radiating crack solutions always coexist with non-radiating dislocation
solutions in solids of quite general anisotropy. Thus, a more thorough study of
supersonic dislocation motion in media of arbitrary anisotropy seems warranted.
In this presentation we show how the solution for a dislocation in uniform
supersonic motion is easily constructed using the formalism of A. N. Stroh [3]
for plane steady problems in generally anisotropic solids. Radiation-free
conditions may be determined by investigating when discarding the supersonic
(or delta wave , in Payton's terminology) terms is possible. This method seems
to us to be more revealing and yields more definitive results than the method
proposed in [2] whereby non-radiation solutions were sought by examining the
retained subsonic terms. We shall present explicit examples of satisfaction of
the radiation-free criteria for anisotropic media. [1] Rosakis, A. J.,
Samudrala, O., and Coker, D., Science, 284, 1337-1340 (1999). [2] Gao, H.,
Huang, Y., Gumbsch, P., and Rosakis, A. J., J. Mech. Phys. Solids, 47,
1941-1961 (1999). [3] Stroh, A. N., Journal of Math. and Physics, 41, 77-103
(1962).

### Friday, May 5, 2000

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior
Secretary, 625-8000.