A model for longitudinal wave propagation in rocks and concrete is presented. Such materials are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. Also known as slow dynamics, the softening of the material is not instantaneous. Based on continuum mechanics with internal variables of state, a new formulation is proposed, which accounts for nonlinear Zener viscoelasticity and softening. A finite-volume method using Roe linearization is developed for the system of partial differential equations so-obtained. The method is used to carry out resonance simulations, and its performance is assessed in the linear viscoelastic case. Qualitative agreement with experimental results of nonlinear ultrasound spectroscopy (NRUS) and dynamic acousto-elastic testing (DAET) is obtained.
Nonlinear acoustics, Softening, Viscoelasticity, Numerical methods