The basic qualitative features of one-dimensional shear shock deformation process are described on the basis of solution of the corresponding evolutionary equation, differing from Hopf equation determining nonlinear dynamics of volumetric deformation. The authors derive the shear evolutionary equation by applying the method of matched asymptotic expansions. This equation defines the solution near the front area of the shock wave. As a generalizing result, the problem of combined axial and torsional loading of a cylindrical cavity is considered. It is shown that even without prior deformations in the medium, the occurrence of the two types of shock waves: the neutral wave and the wave of circular polarization, is possible in such boundary problem. Application the perturbation method to this problem results in a system of two evolutionary equations, with the solutions represented by Riemann invariants.
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