Shock wave propagation in cubic lattices

Abstract

Lattice dynamics has been applied to the study of the propagation of a strong, one-dimensional shock wave in a semi-infinite cubic lattice. The lattice model included the simple cubic, face-centered cubic, and body-centered cubic configurations. The interactions between various neighbors and different types of interactions, ranging from Hooke's law forces to forces corresponding to Morse-type potential functions, were considered. The equations of motion for the lattice points were solved approximately by a numerical method. The results showed that with realistic interatomic forces the computed shock velocity increased with particle velocity approximately in a linear manner, in good qualitative agreement with experimental data. However, because of the dispersive nature of the lattice, it was found that the shock wave profile was unsteady in time, and the computed stresses behind the shock front were different from those obtained under the assumption of a steady shock profile.