Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations

Rocks and concrete are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The proposed system of partial differential equations is solved numerically using finite-volume methods. The numerical tool is used to reproduce qualitatively Nonlinear Resonance Ultrasound Spectroscopy (NRUS) and Dynamic Acoustoelastic Testing (DAET) experiments. A frequency-domain approach based on finite elements, harmonic balance and numerical continuation is compared to the time-domain method. This approach is promising for upcoming experimental validations with respect to resonance experiments.