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

H. Berjamin, B. Lombard, G. Chiavassa, N. Favrie (2018). "A finite-volume approach to 1D nonlinear elastic waves: Application to slow dynamics", Acta Acustica united with Acustica 104(4), 561-570. https://doi.org/10.3813/AAA.919197

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).

FV approach to nonlinear elastodynamics. PACS no. 43.25.Dc, 02.70.Bf