{\mathrm{h}}=\rho_ {\mathrm{0}}U_ {\mathrm{s}}u_ {\mathrm{p}},$$

where $U_\mathrm{s}$ is the shock velocity. It is well known that most materials exhibit a linear relationship between shock velocity and particle velocity, known as the $U_ \mathrm{s}-u_ \mathrm{p}$ Hugoniot. [@Cooper2002] Although this empirical relationship has not been determined for PDMS oils, it is possible to estimate the shock velocity from the ambient speed of sound of the liquid using the so-called *universal Hugoniot* relationship proposed by Woolfolk et al. [@Woolfolk1973]

$$\label{eq:5}
U_ {\mathrm{s}}=1.37c_0-0.37c_0\mathrm{exp}\left(\frac{-2u_\mathrm{p}}{c_0}\right)+1.62u_ \mathrm{p}.$$

It has been shown that this relationship agrees well with a wide variety of liquids as long as the post-shock pressure remains below the bulk modulus of the liquid [@Garrett2006], which is the case in this study.

RESULTS
=======

The test parameters, including the target liquid thickness ($w_\mathrm{l}$), the flyer plate thickness ($w_\mathrm{f}$), and the flyer plate impact velocity ($v_\mathrm{i}$), as well as the resulting maximum particle velocity ($u_\mathrm{max}$) at the free surface, calculated post-shock pressure ($P_\mathrm{h}$), pullback velocity ($\Delta u_\mathrm{fs}$), strain rate ($\dot{\epsilon}$), and measured spall strength ($P_\mathrm{s}$) for 21 plate-impact experiments performed on the PDMS oils are presented in Tab. \[tab:table3\]. The free-surface velocity profiles for the experiments are presented in Fig. \[fig:freesurfacevelocities\], where the curves have been arbitrarily 