1. A finite-volume approach to 1D nonlinear elastic waves: Application to slow dynamics
- Author
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Guillaume Chiavassa, Nicolas Favrie, Bruno Lombard, Harold Berjamin, Ondes et Imagerie ( O&I ), Laboratoire de Mécanique et d'Acoustique [Marseille] ( LMA ), Aix Marseille Université ( AMU ) -Ecole Centrale de Marseille ( ECM ) -Centre National de la Recherche Scientifique ( CNRS ) -Aix Marseille Université ( AMU ) -Ecole Centrale de Marseille ( ECM ) -Centre National de la Recherche Scientifique ( CNRS ), Aix Marseille Université ( AMU ) -Ecole Centrale de Marseille ( ECM ) -Centre National de la Recherche Scientifique ( CNRS ), Ecole Centrale de Marseille ( ECM ), Institut universitaire des systèmes thermiques industriels ( IUSTI ), Centre National de la Recherche Scientifique ( CNRS ) -Aix Marseille Université ( AMU ), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique, Modélisation et Procédés Propres (M2P2), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Institut universitaire des systèmes thermiques industriels (IUSTI), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Lombard, Bruno, Ondes et Imagerie (O&I), and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Acoustics and Ultrasonics ,SCHEMES ,PROPAGATION ,01 natural sciences ,010305 fluids & plasmas ,MEDIA ,symbols.namesake ,Linearization ,INTERNAL VARIABLES ,0103 physical sciences ,010301 acoustics ,[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph] ,Physics ,DAMAGE ,Conservation law ,[SPI.ACOU] Engineering Sciences [physics]/Acoustics [physics.class-ph] ,Finite volume method ,[ SPI.ACOU ] Engineering Sciences [physics]/Acoustics [physics.class-ph] ,Numerical analysis ,Mathematical analysis ,Equations of motion ,[PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph] ,Nonlinear system ,Riemann problem ,symbols ,Flux limiter ,Music - Abstract
International audience; 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).
- Published
- 2018