Wave-Front Analysis in Composite Materials

[+] Author and Article Information
T. C. T. Ting

Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill.

E. H. Lee

Department of Applied Mechanics, Stanford University, Stanford, Calif.

J. Appl. Mech 36(3), 497-504 (Sep 01, 1969) (8 pages) doi:10.1115/1.3564707 History: Received January 27, 1969; Online September 14, 2011


The propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analyzed. Wave front and ray theory analogous to geometrical optics is shown to determine the change in shape of the leading wave front and also the stresses immediately behind it. For certain circumstances the stress amplitudes on this front, or the corresponding tensile stresses on its reflection at the free back surface of a slab, may be critical in design. Examples are presented of an initially sharp plane pressure pulse transmitted through an elastic circular cylinder and an elastic spherical inclusion. The method can be applied to more general composite configurations, and can be extended to determine the stress gradient behind the front. For the latter, general formulas are derived by which the reflection and transmission coefficients can be determined for the stress gradient and the higher-order derivatives at an arbitrary interface.

Copyright © 1969 by ASME
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