Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations

Harold Berjamin; Guillaume Chiavassa; Nicolas Favrie; Bruno Lombard; Emmanuelle Sarrouy

doi:10.1121/2.0000844

Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations

Harold Berjamin
, Guillaume Chiavassa
, Nicolas Favrie
, Bruno Lombard
, Emmanuelle Sarrouy

Research output: Contribution to journal › Conference article › peer-review

Abstract

Rocks and concrete are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The proposed system of partial differential equations is solved numerically using finite-volume methods. The numerical tool is used to reproduce qualitatively Nonlinear Resonance Ultrasound Spectroscopy (NRUS) and Dynamic Acoustoelastic Testing (DAET) experiments. A frequency-domain approach based on finite elements, harmonic balance and numerical continuation is compared to the time-domain method. This approach is promising for upcoming experimental validations with respect to resonance experiments.

Original language	English
Article number	022001
Journal	Proceedings of Meetings on Acoustics
Volume	34
Issue number	1
DOIs	https://doi.org/10.1121/2.0000844
Publication status	Published - 2018
Externally published	Yes
Event	21st International Symposium on Nonlinear Acoustics, ISNA 2018 - Santa Fe, United States Duration: 9 Jul 2018 → 13 Jul 2018

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@article{9dd7bfcdacd74c43b8e45590746508ae,

title = "Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations",

abstract = "Rocks and concrete are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The proposed system of partial differential equations is solved numerically using finite-volume methods. The numerical tool is used to reproduce qualitatively Nonlinear Resonance Ultrasound Spectroscopy (NRUS) and Dynamic Acoustoelastic Testing (DAET) experiments. A frequency-domain approach based on finite elements, harmonic balance and numerical continuation is compared to the time-domain method. This approach is promising for upcoming experimental validations with respect to resonance experiments.",

author = "Harold Berjamin and Guillaume Chiavassa and Nicolas Favrie and Bruno Lombard and Emmanuelle Sarrouy",

note = "Publisher Copyright: {\textcopyright} 2018 Acoustical Society of America.; 21st International Symposium on Nonlinear Acoustics, ISNA 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2018",

doi = "10.1121/2.0000844",

language = "English",

volume = "34",

journal = "Proceedings of Meetings on Acoustics",

issn = "1939-800X",

number = "1",

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TY - JOUR

T1 - Internal-variable modeling of solids with slow dynamics

T2 - 21st International Symposium on Nonlinear Acoustics, ISNA 2018

AU - Berjamin, Harold

AU - Chiavassa, Guillaume

AU - Favrie, Nicolas

AU - Lombard, Bruno

AU - Sarrouy, Emmanuelle

PY - 2018

Y1 - 2018

N2 - Rocks and concrete are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The proposed system of partial differential equations is solved numerically using finite-volume methods. The numerical tool is used to reproduce qualitatively Nonlinear Resonance Ultrasound Spectroscopy (NRUS) and Dynamic Acoustoelastic Testing (DAET) experiments. A frequency-domain approach based on finite elements, harmonic balance and numerical continuation is compared to the time-domain method. This approach is promising for upcoming experimental validations with respect to resonance experiments.

AB - Rocks and concrete are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The proposed system of partial differential equations is solved numerically using finite-volume methods. The numerical tool is used to reproduce qualitatively Nonlinear Resonance Ultrasound Spectroscopy (NRUS) and Dynamic Acoustoelastic Testing (DAET) experiments. A frequency-domain approach based on finite elements, harmonic balance and numerical continuation is compared to the time-domain method. This approach is promising for upcoming experimental validations with respect to resonance experiments.

UR - https://www.scopus.com/pages/publications/85064967758

U2 - 10.1121/2.0000844

DO - 10.1121/2.0000844

M3 - Conference article

AN - SCOPUS:85064967758

SN - 1939-800X

VL - 34

JO - Proceedings of Meetings on Acoustics

JF - Proceedings of Meetings on Acoustics

IS - 1

M1 - 022001

Y2 - 9 July 2018 through 13 July 2018

ER -

Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations

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