Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations

Nicolas Favrie (1) , Bruno Lombard (2) , Cédric Payan (2)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 O&I - Ondes et Imagerie

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.

Mots clés: numerical methods; acoustic conditioning; viscoelasticity; time-dependent materials; hyperbolic system; Nonlinear acoustics

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Analyse numérique [math.NA]

Nicolas Favrie, Bruno Lombard, Cédric Payan. Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations. Wave Motion, 2015, 56, pp.221-238. ⟨hal-01041347v2⟩