Nonlinear Acoustic Waves in Hyperelastic Rods

Excitation of a harmonic wave in a semi-infinite incompressible hyperelastic one-dimensional rod based on the Mooney–Rivlin equation of state shows the formation and propagation of shock wave fronts arising between faster and slower parts of the initially harmonic wave. The observed shock wave fronts lead to the absorption of the slower moving parts by the faster ones, which leads to the attenuation of the kinetic and elastic energy of deformations with the corresponding release of heat. It is found that at a sufficient distance from the edge of the rod, an acoustic black hole arises due to the attenuation of mechanical energy. Geometrically and physically nonlinear equations of motion are solved by an explicit Lax–Wendroff numerical integration scheme in combination with the finite element method for spatial discretization.