Mesoscopic Scale Instability in Particulate Materials

Nicot, François; Veylon, Guillaume; Zhu, Huaxiang; Lerbet, Jean; Darve, Félix

doi:10.1061/(asce)em.1943-7889.0001100

Cited by 11 publications

(11 citation statements)

References 32 publications

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“…Finally, as mentioned and deeply investigated in [], this stiffness tensor is not symmetric which signs the nonconservativeness of the system. This then makes sense to use the Hill criterion as in [].…”

Section: Examplementioning

confidence: 95%

“…In this section, the 4 spheres granular system called the diamond pattern illustrates the above general developments. [] provides an accurate investigation of this granular system with both elastic and elastic‐plastic behaviors. To be in accordance with the framework of the above investigations, only the elastic behavior will be investigated.…”

Section: Examplementioning

confidence: 99%

“…To be in accordance with the framework of the above investigations, only the elastic behavior will be investigated. We roughly take the notations of [] but we adapt them to the present geometrical framework and we follow the same order than for this general framework: kinematics, loading forces, link forces, equilibriums and constitutive laws.…”

Section: Examplementioning

confidence: 99%

“…To focus on the involved geometrical features, some modifications are done with respect to the developments of []. The diamond pattern is a 4 spheres granular system.…”

Section: Examplementioning

confidence: 99%

“…Beyond this systematic proof, it may be obviously remarked that the first equation of is integrable by

N = - k_{n} ℓ

whereas the second one cannot be integrated because

ℓ d α

is not closed and then not exact. As mentioned in [], the purely geometric property that

ℓ d α

is a non closed form is the source of the nonconservativeness of the diamond system. It is directly reflected here in the non integrability of the chosen constitutive laws because of the linearity of these constitutive laws.…”

Section: Examplementioning

confidence: 99%

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Coordinate free nonlinear incremental discrete mechanics

et al. 2018

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In this paper we extend the Kinematic Structural Stability (KISS) issues obtained in the punctual linear case to a full non linear framework. Kinematic Structural Stability (KISS) refers to the stability of conservative or non-conservative elastic systems under kinematic constraints. We revisite and sometimes introduce some new mechanical and geometrically-related concepts, using the systematic language of vector bundles: transversality-stability, tangent stiffness tensor, loading paths and KISS. We bring an intrinsic geometrical meaning to these concepts and we extend the main results to a general nonlinear framework. The lack of connection on the configuration manifold in order to make derivatives of sections is bypassed thanks to the key rule of the nil section of the cotangent bundle. Two mechanical examples illustrate the interest of the new concepts, namely a discrete nonconservative elastic system under nonconservative loading (Ziegler's column) and, in more details, a four-sphere granular system with nonconservative interactions called diamond pattern. K E Y W O R D Scoordinate free approach, fiber bundle, kinematic structural stability, transversality

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Section: Examplementioning

confidence: 95%

Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

“…To focus on the involved geometrical features, some modifications are done with respect to the developments of []. The diamond pattern is a 4 spheres granular system.…”

Section: Examplementioning

confidence: 99%

“…Beyond this systematic proof, it may be obviously remarked that the first equation of is integrable by

N = - k_{n} ℓ

whereas the second one cannot be integrated because

ℓ d α

is not closed and then not exact. As mentioned in [], the purely geometric property that

ℓ d α

Section: Examplementioning

confidence: 99%

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Coordinate free nonlinear incremental discrete mechanics

et al. 2018

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Intrinsic incremental evolution of hypoelastic discrete mechanical systems

et al. 2023

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This paper provides an explicit geometric and coordinate‐free formulation of incremental discrete mechanics in the framework of potentially non integrable hypoelasticity. First, the general framework is developed in order to tackle hypoelasticity as an Ehresmann connection on the cotangent bundle . Two types of incremental evolutions may be distinguished, the weak or integrable incremental evolutions and the strong or non integrable incremental evolutions, according to the nature of the hypoelastic constitutive law. The geometric structure of the double tangent bundle is fully used in order to get the geometric counterpart κ of the so‐called tangent stiffness matrix. Subject to specific conditions in , the incremental evolution is then a well‐founded question. An hypoelastic four‐grains granular system illustrates in detail these general results.

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Force chain collapse as grain column buckling in granular materials

et al. 2017

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International audienceGranular materials react under external loading by self-organizing the topology of the grain assembly. Thus, quasi-linear grain patterns, known as force chains, develop within the assembly to carry the main part of the external loading. The stability of these grain patterns controls the strength of the material, under given loading conditions. This manuscript investigates the mechanical behavior of such grain columns and exhibits some instability modes that can occur even when the local behavior at the contact between grains is purely elastic. First, an analytical approach is developed, and the ability of a grain column to collapse is demonstrated. Then this result is confirmed from numerical simulations performed using a discrete element method

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Mesoscopic Scale Instability in Particulate Materials

Cited by 11 publications

References 32 publications

Coordinate free nonlinear incremental discrete mechanics

Coordinate free nonlinear incremental discrete mechanics

Intrinsic incremental evolution of hypoelastic discrete mechanical systems

Force chain collapse as grain column buckling in granular materials

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