An Extended Continuum Theory for Granular Media

Giovine, Pasquale

doi:10.1007/978-3-540-78277-3_8

Cited by 12 publications

(9 citation statements)

References 35 publications

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“…7 More general continua [31] are obtained by assigning additional kinematic variables to material points, the simplest example being Eringen's microstretch continuum [30] involving dilatation as well as rotation. Although sometimes proposed as a model of granular dilatancy [32,33], the physical significance is not clear. In the typical granular system, the dilatation of individual grains is small compared to that of void space, which is already represented by a simple continuum with variable density or void ratio e. 8 Owing no doubt to the group character of rotations, this relation is much simpler than that connecting the conjugate stress for logarithmic (Hencky) strain to Cauchy stress, as illustrated by the work Xiao et al [41].…”

Section: Kinematics -Rotation and Spinmentioning

confidence: 99%

“…and with corresponding reduction of the quadratic form (32). The further condition of positivity obviously requires inter alia the positivity of µ µ µ 1 and µ µ µ 2 .…”

Section: Elastoplastic Formsmentioning

confidence: 99%

“…with corresponding simplification of (32). Replacing D by T = Σ Σ Σ + ıM and µ µ µ by ζ ζ ζ in (32), one obtains an explicit expression for the Cosserat version of the dissipative yield condition (5):…”

Section: Elastoplastic Formsmentioning

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: Kinematics -Rotation and Spinmentioning

confidence: 99%

“…and with corresponding reduction of the quadratic form (32). The further condition of positivity obviously requires inter alia the positivity of µ µ µ 1 and µ µ µ 2 .…”

Section: Elastoplastic Formsmentioning

confidence: 99%

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Granular hypoplasticity with Cosserat effects

Goddard¹

2010

AIP Conference Proceedings

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“…Different from the Eringen's microcontinuum model, several continuum theories of materials with microstructure have been proposed in the past, among which the Giovine's mathematical model (Giovine, 2008) for a dilatant granular material with rotating grains is closely related to the present work. The Giovine's model is based on the following balance equations for material bodies with affine microstructure (Capriz, 1989;Mariano, 2002) …”

Section: Comparison With the Giovine's Modelmentioning

confidence: 98%

Description of local dilatancy and local rotation of granular assemblies by microstretch modeling

Chen

Lan

Tai

2009

International Journal of Solids and Structures

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a b s t r a c tThis study investigates the microstretch continuum modeling of granular assemblies while accounting for both the dilatant and rotational degrees of freedom of a macroelement. By introducing the solid volume fraction and the gyration radius of a granular system, the balance equations of the microstretch continuum are transformed into a new formulation of evolution equations comprising six variables: the solid volume fraction, the gyration radius, the velocity field, the averaged angular velocity, the rate of gyration radius, and the internal energy. The bulk microinertia density, the averaged angular velocity, and the microgyration tensor at a macroscopic point are obtained in terms of discrete physical quantities. The bulk part and the rotational part of the microgyration tensor are proposed as the two indices to measure the local dilatancy and local rotation of granular assemblies. It is demonstrated in the numerical simulation that the two indices can be used to identify the shear band evolution in a granular system under a biaxial compression.

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“…An interpretation which is in line with an old remark of Toupin [13] on the possibility of viewing hyper-elastic materials of second grade is as Cosserat's continua whose microrotations are constrained (see also Refs. [14][15][16][17][18]).…”

Section: David Publishingmentioning

confidence: 99%

Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

Giovine¹

2017

JMEA

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The thermo-mechanical balance equations for a porous material with big irregular pores are derived from the general ones for a medium with ellipsoidal microstructure by imposing the kinematical constraint of micro-stretch bounded to the macro-deformation: in this case the microstructure disappears apparently (it becomes latent) and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies.

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An Extended Continuum Theory for Granular Media

Cited by 12 publications

References 35 publications

Granular hypoplasticity with Cosserat effects

Granular hypoplasticity with Cosserat effects

Description of local dilatancy and local rotation of granular assemblies by microstretch modeling

Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

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