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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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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