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A finite-volume approach to 1D nonlinear elastic waves: Application to slow dynamics

Abstract : A numerical method for longitudinal wave propagation in nonlinear elastic solids is presented. Here, we consider polynomial stress-strain relationships, which are widely used in nondestructive evaluation. The large-strain and infinitesimal-strain constitutive laws deduced from Murnaghan's law are detailed , and polynomial expressions are obtained. The Lagrangian equations of motion yield a hyperbolic system of conservation laws. The latter is solved numerically using a finite-volume method with flux limiters based on Roe linearization. The method is tested on the Riemann problem, which yields nonsmooth solutions. The method is then applied to a continuum model with one scalar internal variable, accounting for the softening of the material (slow dynamics).
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https://hal.archives-ouvertes.fr/hal-01806373
Contributor : Bruno Lombard Connect in order to contact the contributor
Submitted on : Saturday, June 2, 2018 - 10:52:30 AM
Last modification on : Thursday, November 4, 2021 - 2:44:09 PM
Long-term archiving on: : Monday, September 3, 2018 - 3:59:12 PM

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  • HAL Id : hal-01806373, version 1

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Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. A finite-volume approach to 1D nonlinear elastic waves: Application to slow dynamics. Acta Acustica united with Acustica, Hirzel Verlag, 2018, 104, pp.561-570. ⟨hal-01806373⟩

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