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Pré-Publication, Document De Travail Année : 2014

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

Bruno Lombard
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Cédric Payan

Résumé

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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Dates et versions

hal-01041347 , version 1 (23-07-2014)
hal-01041347 , version 2 (08-12-2014)

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  • HAL Id : hal-01041347 , version 1

Citer

Nicolas Favrie, Bruno Lombard, Cédric Payan. Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations. 2014. ⟨hal-01041347v1⟩
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