First, generalized Rankine–Hugoniot equations for unsteady wave fronts of finite width are derived. It is clarified from these jump equations for particle velocity, stress, and specific internal energy that shock jump conditions involve the effects of rise time of the front or the change in its velocity with time, in addition to that of strain rate and acceleration, and that the treatment in the previous study [Sano, J. Appl. Phys. 82, 5382 (1997)] where the rise time is reduced to an infinitesimal eliminates the terms of this change in the jump equations. Furthermore, the jump equations of the general form derived here support this elimination. Next, the influence of the rise time on the three jumps at the impacted surface of a lithium fluoride single crystal is calculated based on its experimental data and shown to be negligibly small. However, its influence, calculated for sandstone in a similar manner, is great. Finally, a parametric investigation of the influence is carried out for specific strain waves.
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