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, strain-hardening 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 stress-strain diagram of the material for uniaxial strain is supposed to consist of a rectilinear segment followed by a curve that is convex toward the strain-axis. 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 integro-differential equation for the shock path. Closed-form solutions are obtained for two cases. In the first, the suddenly applied stress is thereafter maintained constant, and the curved part of the stress-strain diagram for loading is described by a power law. In the second case, the suddenly applied stress is monotonically reduced to zero, and the stress-strain diagram for loading consists of two straight segments. Finally, a semi-inverse method for obtaining closed-form 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