Abstract
The nonlinear system of hyperbolic equations describing a helical one-dimensional motion of a nonlinear elastic incompressible medium is investigated. Types and velocities of possible divergent shock waves are determined on the basis of a joint analysis of the dynamic compatibility conditions, the characteristics of this system and the Riemann invariants along them. For the single transverse shock wave in previously undeformed medium it is shown that the shearing direction is invariant at the leading shock front determined by the initial action and independent of post-impact loading. The solution of boundary-value problem about shock loading on a circular cylindrical cavity boundary is constructed by the matched asymptotic expansions method and the ray method modified for shock waves.
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