The deformation of an inert confiner by a steady detonation wave in an\ud adjacent explosive is investigated for cases where the confiner is suciently strong\ud (or the explosive suciently weak) such that the overall change in the sound speed\ud of the inert is small. A coupling condition which relates the pressure to the deflection\ud angle along the explosive-inert interface is determined. This includes its dependence\ud on the thickness of the inert, for cases where the initial sound speed of the inert\ud is less than or greater than the detonation speed in the explosive (supersonic and\ud subsonic inert \ud ows, respectively). The deformation of the inert is then solved by\ud prescribing the pressure along the interface. In the supersonic case, the detonation\ud drives a shock into the inert, subsequent to which the \ud ow in the inert consists\ud of alternating regions of compression and tension. In this case reverberations or\ud `ringing' occurs along both the deflected interface and outer edge of the inert. For\ud the subsonic case, the \ud flow in the interior of the inert is smooth and shockless.\ud The detonation in the explosive initially defl\ud ects the smooth interface towards the\ud explosive. For sufficiently thick inerts in such cases, it appears that the deflection\ud of the confiner would either drive the detonation speed in the explosive up to the\ud sound speed of the inert or drive a precursor wave ahead of the detonation in the\ud explosive. Transonic cases, where the inert sound speed is close to the detonation\ud speed, are also considered. It is shown that the confinement affect of the inert on\ud the detonation is enhanced as sonic conditions are approached from either side
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