Theoretical and numerical analysis of the influence of initial stress gradient on wave propagations

The investigation of stress wave propagation in a medium with initial stress has very important application in the field of engineering. However, the previous research less consider the influence of initial stress gradient on wave propagation. In the present paper, the governing equation of wave propagation in elastic continuum material with inhomogeneous initial stress is derived, which indicated that the inhomogeneous initial stress changed the governing equation of wave propagation. Additionally, the definite problem of wave propagation in material with initial stress gradient is verified by using mathematical physics method. Based on the definite problem, the elastic displacement-time relationship of wave propagation is explored, which indicated that the inhomogeneous initial stress changed waveform and relationship of displacement-time histories. Furthermore, the spall process of blasting wave propagation from underground to earth surface is simulated by using LS-DYNA.