Grain-grain collisions and ion sputtering destroy dust grains in interstellar shocks. An analytical theory is developed for the propagation of shock waves in solids driven by grain-grain collisions, which compares very favorably with detailed numerical calculations. This theory is used to determine the fraction of a grain vaporized by a grain-grain collision. Our results predict much less vaporization of colliding grains in interstellar shocks than previous estimates. This theory can also be used to determine the fraction of a colliding grain that melts, shatters, or undergoes a phase transformation to a higher density phase. In particular, the latter two processes can be much more important in interstellar shocks than vaporization. The sputtering of grains by impacting gas ions is reanalyzed based upon extensive laboratory studies and a theoretically derived ``universal\u27\u27 sputtering relation. The analytical results are compared to available experimental studies of sputtering of graphite/amorphous carbon, SiO2, SiC, Fe, and H2O. Sputtering yields for astrophysically relevant materials as a function of impact energy and ion mass are derived. These yields are also averaged over thermal impact spectrum and simple polynomial fits to the resulting yields as a function of temperature are presented. The derived sputtering yields are similar to those adopted in previous studies, except for graphite near threshold where the new yields are much larger due to a lower adopted binding energy. The ion bombardment will amorphitize the surface layers of interstellar grains. It will also convert graphite into hydrogenated amorphous carbon (HAC) to a depth of 10–20 Å. It is suggested that these HAC surfaces are the carriers of the 3.4 µm absorption feature in the interstellar mediu
