Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations
For researchers studying nonlinear dynamics and damage in heterogeneous materials, this model provides a framework to simulate coupled fast-slow processes, though it is incremental as it builds on existing theories.
The paper proposes a physical model for longitudinal vibrations in heterogeneous materials like rocks and concrete, coupling fast nonlinear elastic/viscoelastic dynamics with slow defect evolution, and develops a numerical scheme that shows qualitative agreement with experimental Dynamic Acousto-Elastic Testing.
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a physical model describing the longitudinal vibrations of this class of material, and to develop a numerical strategy for solving the evolution equations. The theory relies on the coupling between two processes with radically-different time scales: a fast process at the frequency of the excitation, governed by nonlinear elasticity and viscoelasticity; a slow process, governed by the evolution of defects. The evolution equations are written as a nonlinear hyperbolic system with relaxation. A time-domain numerical scheme is developed, based on a splitting strategy. The numerical simulations show qualitative agreement with the features observed experimentally by Dynamic Acousto-Elastic Testing.