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A Finite-Volume Approach to 1D Nonlinear Elastic Waves: Application to Slow Dynamics


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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).

Document Type: Research Article

Publication date: July 1, 2018

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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