Nonlinear elasticity in rocks: A comprehensive three-dimensional description

Lott, Martin; Remillieux, Marcel C.; Garnier, Vincent; Le Bas, Pierre-Yves; Ulrich, T. J.; Payan, Cédric

doi:10.1103/PhysRevMaterials.1.023603

Title: Nonlinear elasticity in rocks: A comprehensive three-dimensional description

Abstract

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $$P$$ and (shear) $$S$$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.

Authors:: Lott, Martin; Remillieux, Marcel C.; Garnier, Vincent; Le Bas, Pierre-Yves; Ulrich, T. J.; Payan, Cédric

Publication Date:: Mon Jul 17 00:00:00 EDT 2017

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Fossil Energy (FE); French National Research Agency (ANR)

OSTI Identifier:: 1371610

Alternate Identifier(s):: OSTI ID: 1407887

Report Number(s):: LA-UR-17-23120
Journal ID: ISSN 2475-9953; PRMHAR; 023603

Grant/Contract Number:: AC52-06NA25396; ANR-11 RSNR 0009

Resource Type:: Published Article

Journal Name:: Physical Review Materials

Additional Journal Information:: Journal Name: Physical Review Materials Journal Volume: 1 Journal Issue: 2; Journal ID: ISSN 2475-9953

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 58 GEOSCIENCES; Nonlinear Elasticity, Dynamic Acousto-Elasticity, Geomaterials, Rocks, Hyperelasticity, Slow Dynamics

Citation Formats


                    Lott, Martin, Remillieux, Marcel C., Garnier, Vincent, Le Bas, Pierre-Yves, Ulrich, T. J., and Payan, Cédric. Nonlinear elasticity in rocks: A comprehensive three-dimensional description.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevMaterials.1.023603.

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                    Lott, Martin, Remillieux, Marcel C., Garnier, Vincent, Le Bas, Pierre-Yves, Ulrich, T. J., & Payan, Cédric. Nonlinear elasticity in rocks: A comprehensive three-dimensional description.  United States.  https://doi.org/10.1103/PhysRevMaterials.1.023603

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                    Lott, Martin, Remillieux, Marcel C., Garnier, Vincent, Le Bas, Pierre-Yves, Ulrich, T. J., and Payan, Cédric. Mon .  
"Nonlinear elasticity in rocks: A comprehensive three-dimensional description".  United States.  https://doi.org/10.1103/PhysRevMaterials.1.023603.

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@article{osti_1371610,

  title        = {Nonlinear elasticity in rocks: A comprehensive three-dimensional description},

  author       = {Lott, Martin and Remillieux, Marcel C. and Garnier, Vincent and Le Bas, Pierre-Yves and Ulrich, T. J. and Payan, Cédric},

  abstractNote = {Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.},

  doi          = {10.1103/PhysRevMaterials.1.023603},

  journal      = {Physical Review Materials},

  number       = 2,

  volume       = 1,

  place        = {United States},

  year         = {Mon Jul 17 00:00:00 EDT 2017},

  month        = {Mon Jul 17 00:00:00 EDT 2017}

}

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Title: Nonlinear elasticity in rocks: A comprehensive three-dimensional description

Abstract

Citation Formats

Slow dynamics in the nonlinear elastic response of Berea sandstone journal, October 1996

On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation journal, April 1997

Universal Slow Dynamics in Granular Solids journal, July 2000

Three-dimensional treatment of nonequilibrium dynamics and higher order elasticity journal, April 2016

A unified model of hysteresis and long-time relaxation in heterogeneous materials journal, September 2014

Dynamic triggering of earthquakes journal, October 2005

Pump and probe waves in dynamic acousto-elasticity: Comprehensive description and comparison with nonlinear elastic theories journal, August 2013

Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry: RUS FOR ARBITRARY SHAPE AND HIGH DAMPING journal, July 2015

Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types journal, March 2016

Probing Weak Forces in Granular Media through Nonlinear Dynamic Dilatancy: Clapping Contacts and Polarization Anisotropy journal, February 2004

Measurement of acoustoelastic and third‐order elastic constants for rail steel journal, September 1976

Modeling nonclassical nonlinearity, conditioning, and slow dynamics effects in mesoscopic elastic materials journal, August 2003

Laboratory study of linear and nonlinear elastic pulse propagation in sandstone journal, September 1996

Nonequilibrium and nonlinear dynamics in Berea and Fontainebleau sandstones: Low-strain regime journal, January 2007

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials journal, September 2016

Equation of state and wave propagation in hysteretic nonlinear elastic materials journal, December 1994

Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy journal, June 2013

Finite Deformations of an Elastic Solid journal, April 1937

Measurements of third‐order elastic constants in rocks journal, September 1996

Ultrasonic Study of Three-Phonon Interactions. I. Theory journal, November 1964

Determination of third order elastic constants in a complex solid applying coda wave interferometry journal, January 2009

A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks: RIVIÈRE ET AL. journal, March 2015

Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm journal, April 1995

Ultrasonic Study of Three-Phonon Interactions. II. Experimental Results journal, November 1964

Second-Order Elastic Deformation of Solids journal, December 1953

Nonequilibrium and hysteresis in solids: Disentangling conditioning from nonlinear elasticity journal, March 2010

Characterizing the nonlinear interaction of S- and P-waves in a rock sample journal, January 2015

Memory, relaxation, and microfracturing in dilatant rock journal, July 1981

Structural-change localization and monitoring through a perturbation-based inverse problem journal, November 2014

The effect of cyclic differential stress on dilatancy in westerly granite under uniaxial and triaxial conditions journal, April 1975

Granular crystals: Nonlinear dynamics meets materials engineering journal, November 2015

Soft-ratchet modeling of end-point memory in the nonlinear resonant response of sedimentary rocks journal, May 2005

Concrete cover characterisation using dynamic acousto-elastic testing and Rayleigh waves journal, July 2016

Precursors of Dynamic Excitations and Rupture in Rocks journal, January 2017

Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials journal, April 1999

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone journal, December 2005

Nonlinear and Nonequilibrium Dynamics in Geomaterials journal, August 2004

Quantitative linear and nonlinear resonance inspection techniques and analysis for material characterization: Application to concrete thermal damage journal, August 2014

Resonance and elastic nonlinear phenomena in rock journal, May 1996

CAN: an example of nonclassical acoustic nonlinearity in solids journal, May 2002

Strength Anisotropy of Berea Sandstone: Results of X-Ray Computed Tomography, Compression Tests, and Discrete Modeling journal, August 2015

Nonlinear dynamics induced in a structure by seismic and environmental loading journal, July 2016

Slow dynamics in the nonlinear elastic response of Berea sandstone
journal, October 1996

On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation
journal, April 1997

Universal Slow Dynamics in Granular Solids
journal, July 2000

Three-dimensional treatment of nonequilibrium dynamics and higher order elasticity
journal, April 2016

A unified model of hysteresis and long-time relaxation in heterogeneous materials
journal, September 2014

Dynamic triggering of earthquakes
journal, October 2005

Pump and probe waves in dynamic acousto-elasticity: Comprehensive description and comparison with nonlinear elastic theories
journal, August 2013

Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry: RUS FOR ARBITRARY SHAPE AND HIGH DAMPING
journal, July 2015

Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
journal, March 2016

Probing Weak Forces in Granular Media through Nonlinear Dynamic Dilatancy: Clapping Contacts and Polarization Anisotropy
journal, February 2004

Measurement of acoustoelastic and third‐order elastic constants for rail steel
journal, September 1976

Modeling nonclassical nonlinearity, conditioning, and slow dynamics effects in mesoscopic elastic materials
journal, August 2003

Laboratory study of linear and nonlinear elastic pulse propagation in sandstone
journal, September 1996

Nonequilibrium and nonlinear dynamics in Berea and Fontainebleau sandstones: Low-strain regime
journal, January 2007

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials
journal, September 2016

Equation of state and wave propagation in hysteretic nonlinear elastic materials
journal, December 1994

Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy
journal, June 2013

Finite Deformations of an Elastic Solid
journal, April 1937

Measurements of third‐order elastic constants in rocks
journal, September 1996

Ultrasonic Study of Three-Phonon Interactions. I. Theory
journal, November 1964

Determination of third order elastic constants in a complex solid applying coda wave interferometry
journal, January 2009

A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks: RIVIÈRE ET AL.
journal, March 2015

Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm
journal, April 1995

Ultrasonic Study of Three-Phonon Interactions. II. Experimental Results
journal, November 1964

Second-Order Elastic Deformation of Solids
journal, December 1953

Nonequilibrium and hysteresis in solids: Disentangling conditioning from nonlinear elasticity
journal, March 2010

Characterizing the nonlinear interaction of S- and P-waves in a rock sample
journal, January 2015

Memory, relaxation, and microfracturing in dilatant rock
journal, July 1981

Structural-change localization and monitoring through a perturbation-based inverse problem
journal, November 2014

The effect of cyclic differential stress on dilatancy in westerly granite under uniaxial and triaxial conditions
journal, April 1975

Granular crystals: Nonlinear dynamics meets materials engineering
journal, November 2015

Soft-ratchet modeling of end-point memory in the nonlinear resonant response of sedimentary rocks
journal, May 2005

Concrete cover characterisation using dynamic acousto-elastic testing and Rayleigh waves
journal, July 2016

Precursors of Dynamic Excitations and Rupture in Rocks
journal, January 2017

Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials
journal, April 1999

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone
journal, December 2005

Nonlinear and Nonequilibrium Dynamics in Geomaterials
journal, August 2004

Quantitative linear and nonlinear resonance inspection techniques and analysis for material characterization: Application to concrete thermal damage
journal, August 2014

Resonance and elastic nonlinear phenomena in rock
journal, May 1996

CAN: an example of nonclassical acoustic nonlinearity in solids
journal, May 2002

Strength Anisotropy of Berea Sandstone: Results of X-Ray Computed Tomography, Compression Tests, and Discrete Modeling
journal, August 2015

Nonlinear dynamics induced in a structure by seismic and environmental loading
journal, July 2016