Accession Number:

AD0679653

Title:

ANALYSIS OF WAVE PROPAGATION IN A NONLINEAR STRAIN HARDENING MEDIUM,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF THE AEROSPACE AND MECHANICAL ENGINEERING SCIENCES

Personal Author(s):

Report Date:

1968-09-01

Pagination or Media Count:

39.0

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

Subject Categories:

  • Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE