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

Abstract : 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.
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Submitted on : Monday, December 8, 2014 - 3:25:09 PM
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  • HAL Id : hal-01041347, version 2
  • ARXIV : 1412.2979

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

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