Bilinear Theories in Plasticity and an Application to Two-Dimensional Wave Propagation

[+] Author and Article Information
H. R. Aggarwal, A. M. Soldate, J. F. Hook

National Engineering Science Company, Pasadena, Calif.

Julius Miklowitz

California Institute of Technology, Pasadena, Calif.; National Engineering Science Company

J. Appl. Mech 31(2), 181-188 (Jun 01, 1964) (8 pages) doi:10.1115/1.3629584 History: Received April 05, 1963; Online September 15, 2011


The Koehler and Seitz bilinear theory is generalized and related to a similar theory given by Swainger. It is shown that, in contradistinction to the corresponding Hencky theory, the generalized theory depends partially on the strain path, and further leads to linearization of the governing equations. An alternative form analogous to the generalized Hooke’s law is given. Displacement equations of motion for the bilinear model are derived and explicit expressions for plastic wave velocities obtained. Dynamic equations for cases previously considered in the literature are compared. As an application, the initial stress discontinuities for the problem of scattering of a plane compressional step wave by a rigid, perfectly dense cylinder are obtained.

Copyright © 1964 by ASME
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