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A Unified Treatment of Nonlinear Viscoelasticity and Non-equilibrium Dynamics

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Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation

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Abstract

This chapter introduces bases of nonlinear mesoscopic elasticity and presents a novel approach to model and numerically simulate the dynamical behavior of this class of material. Under dynamical solicitation, these so-called nonclassical materials exhibit two different time-dependent nonlinear mechanisms termed “fast” (nonlinear elasticity) and “slow” (loss of elastic properties and relaxation). A unified model of one-dimensional continuum is presented, which combines all of these phenomena as well as viscoelastic attenuation often neglected. The final set of partial differential equations is a system of conservation laws with relaxation described by a reduced number of parameters to account for all the effects. A numerical scheme based on finite-volume methods is presented which reproduces well the key experimental observations made in Dynamic Acousto Elasticity (DAE) and Nonlinear Resonant Ultrasound Spectroscopy (NRUS) type of experiments.

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Acknowledgements

This work was supported by the interdisciplinary mission of CNRS (INFINITI). The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University—A*MIDEX, a French “Investissements d’Avenir” programme. It has been carried out in the framework of the Labex MEC.

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Authors and Affiliations

  1. Aix Marseille Univ, CNRS, Centrale Marseille, LMA, Marseille, France

    H. Berjamin, B. Lombard & C. Payan

  2. Aix Marseille Univ, CNRS, IUSTI, Marseille, France

    N. Favrie

  3. Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France

    G. Chiavassa

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  1. H. Berjamin
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  2. G. Chiavassa
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  3. N. Favrie
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  4. B. Lombard
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  5. C. Payan
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Corresponding author

Correspondence to C. Payan .

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Editors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, USA

    Tribikram Kundu

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Berjamin, H., Chiavassa, G., Favrie, N., Lombard, B., Payan, C. (2019). A Unified Treatment of Nonlinear Viscoelasticity and Non-equilibrium Dynamics. In: Kundu, T. (eds) Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation. Springer, Cham. https://doi.org/10.1007/978-3-319-94476-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-94476-0_11

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