Appearing shock waves in Arruda – Boyce incompressible rod

Abstract

The Arruda – Boyce incompressible hyperelastic potentials are used for analyzing one-dimensional acoustic wave propagation in a semi-infinite nonlinearly elastic rod. It has been found that during the propagation of the delta-like pulses, the following phenomena are observed, (i) the shock wave fronts arise; (ii) the pulses spread out due to physical dispersion; (iii) the mechanical energy of the considered system decreases with time, resulting in a decrease of the pulse magnitudes; and, at the same time (iv) thermal energy arises and increases with time, that is caused by formation and propagation of shock wave fronts. The analysis utilizes a combined method consisting of the explicit time integration technique coupled with the finite element method for spatial discretization.