Riemann waves in an elastic medium with small cubic anisotropy

Shock waves in an elastic medium with cubic anisotropy

“…According to the results obtained previously in Ref. 5 for the slow waves this is the direction in which k decreases. This means that the initial point must be on the right of the points considered, for which k > k(E).…”

“…sections of the shock adiabatic in the neighbourhood of the initial point coincide with the elements of the integral curves of Riemann waves, which were obtained previously in Ref. 5 for system of Eq. (2.1), and the following expressions were obtained for the characteristic velocities (2.6) corresponding to slow Riemann waves (c 1 ) and fast Riemann waves (c 2 ).…”

“…4. When using the components of the gradients of the displacement u i instead of ij for waves propagating along the principal diagonal of the cube, the elastic potential of an incompressible medium must be taken in the form 5 (1.1)…”

“…It was shown in Ref. 5 that for a medium of this type, the change in u 3 can be expressed in terms of the change in u 1 and u 2 . This applies similarly for [u 3 ].…”

Deformations in Micropolar Thermoelastic Medium Possessing Cubic Symmetry Due to Inclined Loads

“…Panait [22] investigated the conditions of plane wave propagation in cubic crystals subject to initial deformations and electric fields. Sveshnikova [23,24] discussed the wave propagation of a cube in an incompressible elastic medium possessing cubic symmetry. Norris [25] examined the wave fronts from a point source in a solid with cubic symmetry.…”