Bulk waves in nonlinear compressible materials

Abstract

Bulk plane waves propagating in a compressible hyperelastic medium are analyzed. The medium is modeled by the Ogden compressible hyperelastic potential, which is often used for analyzing compressible foams. It is revealed that during the propagation of a delta-shaped pulse, strong shock wave fronts are formed and start to propagate, causing several interesting phenomena, including (i) substantial attenuation of the propagating acoustic waves with distance; (ii) the formation of shock wave fronts travelling at a slower velocity than the maximal P-wave velocity; and, (iii) heat release caused by the appearance of shock wave fronts. The uncovered phenomena can explain the experimentally observed dissipation of mechanical energy accompanying the propagation of bulk waves in foams.