A nonlinearly thermoelastic half-space under time-dependent normal and shear loading

A nonlinearly thermoelastic half-space is subjected to combined time-dependent normal and shear loading. The solution is obtained by a numerical method which is shown to yield accurate results by comparison with some known analytical solutions which can be obtained in some special cases. When shocks are involved, it is shown that the numerical results satisfy all the Rankine-Hugoniot jump conditions as well as the entropy condition across the shock.