Unsteady plane smooth wave fronts of combined growing-attenuating type

Abstract

Compression and shear wave measurements to characterize the shocked state in silicon carbideUnsteady plane smooth wave fronts of a combined growing-attenuating type, where the peak of each strain wave is growing, are derived by a qualitative analysis. There are three different modes in this combined type: In mode I, the peak of a particle velocity wave is growing, but that of a stress wave is attenuating; in mode II, the former is attenuating, but the latter is growing; in mode III, both are attenuating. Three possible wave fronts belong to mode I, five to mode II, and three to mode III. Five new elementary waves are found in these eleven wave fronts. The wave fronts near the impacted surface of sandstone detected by the previous quantitative analysis ͓Sano, J. Appl. Phys. 73, 118 ͑1993͔͒ are identified with some of the eleven possible wave fronts. As a result, the theoretical existence of several new wave fronts and a new elementary wave is verified. The equation for the stress at the impacted surface indicates that strain acceleration is responsible for the formation of the wave fronts of the combined type, which cause an anomalous response, and hence it should be included in the constitutive relations which describe the response.

Generalized smooth and weak-discontinuous unsteady waves

“…It was recently clarified that the effects of the strain rate and strain acceleration induce smooth or weak-discontinuous unsteady wave fronts in those materials and they are responsible for anomalous stress-particle velocity and stress-strain paths. [5][6][7][8][9][10][11][12][13][14][15] In addition, Rankine-Hugoniot jump conditions 16,17 can only be applied insufficiently to some unsteady wave fronts that induce nonzero strain accelerations. 13,14 Use of these jump conditions in translating particle velocity into stress is one of the factors that causes the precursor decay anomaly in single-crystal lithium fluoride.…”

“…where b ii 0 and c iiϩ1 0; iϭ1,2,...,n. This generalization of the previous plane wave theory [5][6][7][8][9][10][11][12][13][14][15] using the conservation equations of mass and momentum also considers that B, C, and d depend on ũ, x, and t, respectively. The fundamental theorem demonstrates the theoretical existence of a smooth wave and a weak-discontinuous wave in a generalized wave.…”

Shock jump equations for unsteady wave fronts of finite rise time

“…[12][13][14][15] This means that shock jumps depend on strain rate and acceleration as well as strain. Therefore, we must introduce strain rate and acceleration into shock jump conditions.…”