Constraints on Moving Strong Discontinuity Surfaces in Dynamic Plane-Stress or Plane-Strain Deformations of Stable Elastic-Ideally Plastic Materials

[+] Author and Article Information
Yinong Shen, W. J. Drugan

Department of Engineering Mechanics, University of Wisconsin, Madison, WI 53706

J. Appl. Mech 57(3), 569-576 (Sep 01, 1990) (8 pages) doi:10.1115/1.2897060 History: Received December 21, 1988; Revised July 01, 1989; Online March 31, 2008


For dynamic deformations of compressible elastic-ideally plastic materials in the practically important cases of plane stress and plane strain, we investigate the possible existence of propagating surfaces of strong discontinuity (across which components of stress, strain, or material velocity jump) within a small-displacement-gradient formulation. For each case, an explicit proof of the impossibility of such a propagating surface (except at an elastic wave speed) is achieved for isotropic materials satisfying a Huber-Mises yield condition and associated flow rule, and we show that our method of proof can be generalized to a large class of anisotropic materials. Nevertheless, we demonstrate that moving surfaces of strong discontinuity cannot be ruled out for all stable (i.e., satisfying the maximum plastic work inequality) materials, as in the case of a material whose yield surface contains a linear portion. A clear knowledge of the conditions under which dynamically propagating strong discontinuity surfaces can and cannot exist is crucial to the attainment of correct and complete solutions to such practical elastic-plastic problems as dynamic crack propagation, impact and rapidly moving load problems, high-speed forming, cutting, and other manufacturing processes.

Copyright © 1990 by The American Society of Mechanical Engineers
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