Numerical study on patterning of shear bands in a Cosserat continuum

Tejchman, J.; Wu, Wei

doi:10.1007/bf01177235

Cited by 126 publications

(76 citation statements)

References 24 publications

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“…While the model does not identify a yield surface per se, the "stationary state" where stress rate vanishes represents the dissipative yield surface identified in the present work, subject to the interpretation of µ µ µ H and N in (6). Furthermore, and contrary to occasional remarks in the literature, hypoplasticity does allow for elastic response, provided that term N become negligible for small |T|, which is suggested immediately by the form of (6).…”

Section: Nonpolar Hypoplasticitymentioning

confidence: 67%

“…Special cases of this appear in several past works [6,44,9], with some of the prior history given by Tejchman [2,Chapt. 3].…”

Section: Elastoplastic Formsmentioning

confidence: 99%

“…For example in the case of void ratio e, the power is given by pė/(1 + e), where p = −tr(T)/3, whereas for accumulated plastic shear γ P defined by (13) 6 , it is easy to show that the power is given by τ PγP , with τ P = T : κ κ κ P : T.…”

Section: Passive Vs Active Variablesmentioning

confidence: 99%

“…That work does not provide a complete description of strain-induced evolution of anisotropy, and a cursory survey of subsequent literature suggests that, with notable exceptions [24], attempts are rarely made to relate micro-level to continuum-level descriptions of texture evolution. 6 Conversely, given any norm τ = | |T| |, one can defineγ P =D : µ µ µ P :D/τ, which appears equivalent to Hill's [26] duality based on plastic potentials.…”

Section: Passive Vs Active Variablesmentioning

confidence: 99%

“…As mentioned in the Abstract, many special cases of the Cosserat model are to be found in the literature [4,5,6,7,8,9,10,11]. Much of the history and many theoretical concepts are covered in the recent monograph of Tejchman [2], which is focused on numerical simulations of soil mechanics based on standard hypoplastic modeling.…”

Section: Introductionmentioning

confidence: 99%

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Granular hypoplasticity with Cosserat effects

Goddard¹

2010

AIP Conference Proceedings

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Abstract. This paper provides an extension to Cosserat mechanics of a recently proposed version of hypoplasticity [1], and this extension is achieved economically by means of a novel complex-variable formulation of Cosserat theory.The present work represents a compact synthesis and theoretical framework for both non-polar and polar hypoplasticity, and it encompasses various special cases considered in the literature, as discussed in the recent monograph by Tejchman [2].The current approach offers a perspective on granular dilatancy, elastoplastic yield, and energy dissipation which differs from the standard hypoplasticity and which serves to establish a connection to classical incremental plasticity. In contrast to the classical theory, the present approach, based entirely on the concept of pseudo-linear forms, admits but does require elastoplastic potentials to describe plastic flow. When such potentials are assumed, it is shown that they can be related to the plastic moduli of the present formulation.It is also shown that hypoplasticity allows for a distinction between active and passive internal variables, with the latter serving to define parameters. Finally, the known forms for linear isotropic Cosserat elasticity are employed to represent isotropic hypoplasticity, and the resulting formulae appear to encompass several empiricisms found in the literature.

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Section: Nonpolar Hypoplasticitymentioning

confidence: 67%

“…Special cases of this appear in several past works [6,44,9], with some of the prior history given by Tejchman [2,Chapt. 3].…”

Section: Elastoplastic Formsmentioning

confidence: 99%

Section: Passive Vs Active Variablesmentioning

confidence: 99%

Section: Passive Vs Active Variablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Granular hypoplasticity with Cosserat effects

Goddard¹

2010

AIP Conference Proceedings

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FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localization

Tejchman

Herle

Wehr³

1999

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

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SUMMARYThe paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The in#uence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a "nite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FEcalculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar e!ects manifested by the appearance of grain rotations and couple stresses are only signi"cant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement.

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Shearing of a narrow granular layer with polar quantities

Tejchman

Gudehus²

2000

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

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SUMMARYThe paper deals with numerical investigations of the behaviour of granular bodies during shearing. Shearing of a narrow layer of sand between two very rough boundaries under constant vertical pressure is numerically modelled with a "nite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localization. The material constants can be easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the in#uence of the initial void ratio, pressure level, mean grain diameter and grain roughness on the thickness of shear zones. The results of shearing are also compared to solutions without the polar extensions. The FE-calculations demonstrate that polar e!ects manifested by the appearance of grain rotations and couple stresses are signi"cant in the shear zone, and its thickness is sensitive to the initial void ratio, mean grain diameter and layer height. The e!ect of the pressure level is rather low within the considered range.

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Numerical study on patterning of shear bands in a Cosserat continuum

Cited by 126 publications

References 24 publications

Granular hypoplasticity with Cosserat effects

Granular hypoplasticity with Cosserat effects

FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localization

Shearing of a narrow granular layer with polar quantities

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