Temmen<i>et al.</i>Reply:

Temmen, Hubert; Pleiner, Harald; Liu, Mario; Brand, Helmut R.

doi:10.1103/physrevlett.86.745

Cited by 21 publications

(37 citation statements)

References 3 publications

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“…In this equation, the term (u ik ∇ j v k )+(i ↔ j), important for large strain field and frequently negligible for hard grains, is of geometric origin, see [59][60][61][62] for explanations. The dissipative flux y i ∼ ∇ j π i j will be derived in Sect.…”

Section: Elastic and Plastic Strainmentioning

confidence: 99%

“…Transiently elastic media such as polymers are under active consideration at present [59][60][61][62]. Constructing a granular hydrodynamic theory, we believe, is both useful and possible: useful, because it should help to illuminate and order the complex macroscopic behavior of granular solid; possible, because total energy is conserved in granular media, as it is in any other system.…”

Section: Introductionmentioning

confidence: 99%

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Granular solid hydrodynamics

2009

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A complete continuum mechanical theory for granular media, including explicit expressions for the energy current and the entropy production, is derived and explained. Its underlying notion is: granular media are elastic when at rest, but turn transiently elastic when the grains are agitatedsuch as by tapping or shearing. The theory includes the true temperature as a variable, and employs in addition a granular temperature to quantify the extent of agitation. A free energy expression is provided that contains the full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. We refer to the theory as GSH, for granular solid hydrodynamics. In the static limit, it reduces to granular elasticity, shown previously to yield realistic static stress distributions. For steady-state deformations, it is equivalent to hypoplasticity, a state-of-the-art engineering model.

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Section: Elastic and Plastic Strainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Granular solid hydrodynamics

2009

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“…There, they resulted from the requirement that the physics be independent of the orientation of the system (as long as external fields are absent or likewise reoriented) [48,49,55]. For a = 1, the form (39) and (53) is typically referred to as the lower convected derivative [54,55].…”

Section: A Reversible Dynamicsmentioning

confidence: 99%

Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables

Menzel

2016

Phys. Rev. E

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One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a new macroscopic variable: relative strains. We analyze two simplified minimal example geometries as an illustration.

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“…In case of a transient elasticity, this strain field relaxes on the long time scale. The consequences of the approach of transient elasticity for complex fluids such as polymer solutions and melts have been investigated in the linear [29,30] as well as in the nonlinear regime [31][32][33][34][35][36][37] for systems ranging from polymer melts and solutions [29, 31-34, 36, 37] over nematic polymers [30,35] to ferrocholesteric gels and elastomers [38]. Quite recently the applicability of the theory of transient elasticity to a large range of rheologically important small and large amplitude experiments has also been demonstrated [39,40].…”

Section: Macroscopic Dynamicsmentioning

confidence: 99%

On the influence of a network on optically isotropic fluid phases with tetrahedral/octupolar order

Brand

Pleiner

2017

Eur. Phys. J. E

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Abstract.We investigate the influence of transient or permanent elasticity on liquid phases with octupolar (tetrahedral) order, a question that has never been addressed before. The focus will be on optically isotropic liquid phases with tetrahedral order including the T d phase and the chiral T phase introduced by Fel. It turns out that the presence of both, a network as well as tetrahedral order can lead to the formation of chiral domains of both hands in an optically isotropic fluid due to a completely novel mechanism, thus providing a possible macroscopic explanation for recent experimental observations. We study in detail how elasticity influences the macroscopic dynamics of both, the T d and the T phase. The simultaneous presence of a transient network as well as of octupolar order is shown to lead to completely new crosscoupling phenomena for optically isotropic systems including transient dissipative elastic strains due to temperature gradients.

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Temmenet al.Reply:

Cited by 21 publications

References 3 publications

Granular solid hydrodynamics

Granular solid hydrodynamics

Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables

On the influence of a network on optically isotropic fluid phases with tetrahedral/octupolar order

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