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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Acta Acustica united with Acustica, Hirzel Verlag, 2018, 104, pp.561-570
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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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