Energy localization in rapidly deforming crystalline solids

The localization of both energy and deformation plays a central role in determining the response of crystalline solids to rapid shear deformation. Here we examine on a microstructural level a process by which this localization can occur by determining the rate at which energy is dissipated by moving edge dislocations. To first order, the rate of energy dissipation is shown to be proportional to the deformation velocity and to be very large at high rates of deformation (≊${10}^7$ erg/s per cm of moving dislocation). At even higher rates, typical of shocks, the second- and higher-order terms dominate the energy dissipation process, and these can lead to direct or multiphonon excitation of the internal modes of the molecules in the crystal. These latter processes may have an important role in the rapid molecular dissociation that occurs during detonations, while the first-order terms are influential in determining the yielding and shear-band formation in crystals.