Abstract
An increase in the stiffness of a solid in compression is known to lead to the steepening of the profiles of compression waves and, as a consequence, to the formation of strong discontinuities from continuous waves propagating in the solid. In this paper, the critical distance required for a continuous wave to turn into a shock wave is calculated from the evolution equation for a weak discontinuity (acceleration wave) propagating into a quiescent region. Infinite growth of the amplitude of an acceleration wave in a finite time signifies the transition to a strong discontinuity. Relations between the critical distances for plane, cylindrical and spherical waves are established. Numerical examples are presented for a particular case of the pressure-dependent stiffness typical of granular solids such as sand or soil, with emphasis placed on the influence of a small amount of free gas in the pore fluid.
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