University of Minnesota
Aerospace Engineering and Mechanics
Spring 2000 Seminar Series



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


Prof. David Barnett

Department of Materials Science and Engineering, Stanford University


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.