
Accession Number : AD0679653
Title : ANALYSIS OF WAVE PROPAGATION IN A NONLINEAR STRAIN HARDENING MEDIUM,
Corporate Author : CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF THE AEROSPACE AND MECHANICAL ENGINEERING SCIENCES
Personal Author(s) : Shieh,R. C.
Report Date : SEP 1968
Pagination or Media Count : 39
Abstract : The paper is concerned with the propagation of plastic waves of uniaxial strain across an infinite, nonlinear, strainhardening slab of finite thickness that is free at one surface and subjected, at the other, to a suddenly applied compressive stress, which thereafter is maintained constant or decreased monotonically to zero. In loading, the stressstrain diagram of the material for uniaxial strain is supposed to consist of a rectilinear segment followed by a curve that is convex toward the strainaxis. In unloading, the strain is supposed to remain constant (rigid unloading). General expressions for stress, strain, and particle velocity are derived, together with the governing integrodifferential equation for the shock path. Closedform solutions are obtained for two cases. In the first, the suddenly applied stress is thereafter maintained constant, and the curved part of the stressstrain diagram for loading is described by a power law. In the second case, the suddenly applied stress is monotonically reduced to zero, and the stressstrain diagram for loading consists of two straight segments. Finally, a semiinverse method for obtaining closedform solutions is developed in which the applied stress is treated as a function of the shock path so that the determination of its explicit variation with time is a part of the solution of the problem. (Author)
Descriptors : (*SHOCK WAVES, PROPAGATION), STRAIN(MECHANICS), EQUATIONS OF MOTION, STRAIN HARDENING, STRESSES, DIFFERENTIAL EQUATIONS
Subject Categories : Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE