Symchuk I. Features of the propagation of cylindrical waves in hyperelastic materials with an internal structure

The thesis is devoted to studing the propagation of cylindrical waves in hyperelastic composite materials. The nonlinear wave equations are derived for different representations of the elastic potential, which correspond to two distinguishing microstructural models of composite materials – the model of effective elastic moduli and the model of two-phase elastic mixture. The approximate solutions are obtained for the radial cylindrical waves basing on the Hankel functions and for the torsional cylindrical waves basing on the Bessel functions. The computer modeling of evolution of both the radial cylindrical waves, and the torsional cylindrical waves is carried out for cases of isotropic and transversely isotropic materials. On basis of results of modeling, the scenarios of evolution are constructed and the comparison of obtained for Murnaghan and Signorini potentials results is carried out for cases "plane wave – cylindrical wave", "cylindrical wave – cylindrical wave".