The Propagation of an Impulse Into a Viscous-Locking Medium

Abstract

A viscous-locking medium is defined by the compressive stress-strain relation p = f(ε) + μεt , where f(ε) = 0 for ε < εc and f′ (εc ) = ∞; it behaves as a viscous liquid until the compressive strain attains the value εc , after which it behaves as a rigid solid. A general solution is given for the disturbance produced by a pressure p0 (t) acting on an inviscid (μ = 0) half space, in which case the transition from viscous to rigid phases occurs through a shock wave. It is found that the stress falls off inversely as the square of the depth of penetration and that it may be approximated (asymptotically) by the disturbance produced by a concentrated impulse. A similarity solution then is given for a concentrated impulse acting on a viscous half space. It is concluded that viscosity reduces the peak pressure at all depths, even though the disturbance is diffused into the viscous phase and may achieve its peak value in that phase.