Granular Elasticity without the Coulomb Condition

Jiang, Yimin; Liu, Mario

doi:10.1103/physrevlett.91.144301

Cited by 77 publications

(82 citation statements)

References 19 publications

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“…This hypothesis is in accordance with the recent successful modeling of static behavior of unconsolidated granular materials [41,42], where the important assumption was the dependence of all elastic moduli on pressure. In quadratic approximation of nonlinear acoustics the static stress/strain relationships proposed in [41,42] reproduce the nonlinear term in equation (11) and predict also an additional nonlinear term proportional to square of the shear strain, if the shear strain exists simultaneously with longitudinal one. The additional term describes the generation of longitudinal waves due to effect of dilatancy [24,41,42].…”

Section: Quadratic Approximation Of Nonlinear Acoustics For An Unconssupporting

confidence: 74%

“…The static stress/strain relationship proposed in [41,42] does not reproduce hysteretic quadratic nonlinear term in equation (21), because hysteresis is a dynamic phenomenon. But the stress/strain law from [41,42] adds in equation (21) a quadratic term proportional to the product of longitudinal and shear strains, which describes the modulation of the shear modulus by longitudinal wave, but does not contribute to self-action of shear waves in the quadratic approximation.…”

Section: Quadratic Approximation Of Nonlinear Acoustics For An Unconsmentioning

confidence: 99%

“…In quadratic approximation of nonlinear acoustics the static stress/strain relationships proposed in [41,42] reproduce the nonlinear term in equation (11) and predict also an additional nonlinear term proportional to square of the shear strain, if the shear strain exists simultaneously with longitudinal one. The additional term describes the generation of longitudinal waves due to effect of dilatancy [24,41,42]. The static stress/strain relationship proposed in [41,42] does not reproduce hysteretic quadratic nonlinear term in equation (21), because hysteresis is a dynamic phenomenon.…”

Section: Quadratic Approximation Of Nonlinear Acoustics For An Unconsmentioning

confidence: 99%

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Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

Gusev¹,

Aleshin²,

Tournat³

2008

Acta Acustica united with Acustica

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SummaryThe problem of the nonlinear reflection of acoustic waves from a mechanically free surface of an unconsolidated granular layer under gravity is solved analytically using the successive approximations method. The theory revealed specific dependencies of the characteristics of the generated acoustic harmonics of longitudinal and shear waves on frequency and the thickness of the granular layer, which are related to a power-law gravity-induced depth stratification of linear and nonlinear mechanical properties of the granular layer. The developed theory could be useful for the analysis of the acoustic experiments directed to the investigation of fundamental mechanical properties of unconsolidated granular media near the jamming transition taking place at zero confining pressure.

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Section: Quadratic Approximation Of Nonlinear Acoustics For An Unconssupporting

confidence: 74%

Section: Quadratic Approximation Of Nonlinear Acoustics For An Unconsmentioning

confidence: 99%

Section: Quadratic Approximation Of Nonlinear Acoustics For An Unconsmentioning

confidence: 99%

See 1 more Smart Citation

Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

Gusev¹,

Aleshin²,

Tournat³

2008

Acta Acustica united with Acustica

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“…Next, it should be interesting to use gsh for circumstances, in which T g is not stationary and the stress rate possesses a more complicated form than that given by Eqs (3,15,16).…”

Section: Figmentioning

confidence: 99%

“…Starting from this observation, a theory termed ge (for "granular elasticity") was constructed to account for static granular stress distributions. Taking the energy w as a function of u ij , the elastic contribution to the total strain field ε ij , we specify [3] …”

mentioning

confidence: 99%

From Elasticity to Hypoplasticity: Dynamics of Granular Solids

Jiang

Liu

2007

Phys. Rev. Lett.

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A fully coupled THM model based on a non-equilibrium thermodynamic approach and its application

Zhang

Cheng

2016

Int. J. Numer. Anal. Meth. Geomech.

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In this study, a fully coupled thermo-hydro-mechanical (THM) theoretical model, called the TSINGHUA-THERMOSOIL model, which is applicable in saturated soils, was developed based on a non-equilibrium thermodynamic approach (see Groot S, Mazur P. Non-Equilibrium thermodynamics. Amsterdam: North-Holland Pub. Co., 1962). This model simplifies the mathematical description of a THM coupling system to the modeling of a group of migration coefficients and energy functions by means of the nonequilibrium thermodynamic theory. The important concept of granular entropy was introduced for describing the granular fluctuation and the resulting transient elasticity. Therefore, non-elastic mechanical constitutive relations that do not require such concepts as yield surface and flow rule are obtained. The physical process of bound pore water transforming into free water when the temperature rises was taken into consideration for describing the phenomenon of the volumetric compression of normally consolidated and slightly over-consolidated clays under non-isothermal conditions. The behavior of thermal consolidation and drained shear tests at different temperatures for saturated Kaolin clay with different over-consolidation ratios (OCR) were simulated using this model. The effect of the OCR value, the heating rate and temperature cycling on the thermal consolidation and the effect of the temperature on the shear strength were analyzed and compared with existing experimental data. The results showed that the model proposed in this paper can accurately describe the thermal consolidation and the basic law of shearing for saturated soil, which preliminarily proves the validity of the model. the constitutive relations are derived from the constraints between the conservation laws and the thermodynamic principles. The relationships between state variables are derived through the definitions of certain thermodynamic potential functions. The famous Onsager reciprocal relation [27], involving a set of migration coefficients and dissipative forces, is used to quantify the energy dissipations. This approach can be very useful to find the connections between the THM coupling laws and the physical mechanisms in the coupling processes. Therefore, it is employed in this paper to establish a THM model for saturated soils. In this model, the elastic potential energy function plays an important role on the mechanical constitutive relations, and the energy dissipation at particulate level, usually called granular fluctuation [25], is considered and linked with the unrecoverable deformation. Another point of this model is to find the theoretical relationship between the heating-induced conversion of bound water to free water and the thermo-plasticity, in which the cyclic effect is also considered. Based on this model, many important THM coupling features, such as the over-consolidation ratio (OCR) dependency, the rate dependency, the cyclic THM COUPLED SOIL MODEL 529The specific entropies can be defined as a function of temperature, as shown in Eqs. 8b...

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Granular Elasticity without the Coulomb Condition

Abstract: A self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.

Cited by 77 publications

References 19 publications

Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

From Elasticity to Hypoplasticity: Dynamics of Granular Solids

A fully coupled THM model based on a non-equilibrium thermodynamic approach and its application

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