On the definition of the stress tensor in granular media

Nicot, François; Hadda, Nejib; Guessasma, Mohamed; Fortin, Jérôme; Millet, Olivier

doi:10.1016/j.ijsolstr.2013.04.001

Cited by 87 publications

(66 citation statements)

References 15 publications

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“…Numerous works in the last decade have been devoted to the definition of the mean stress tensor in multi-contacts systems [27,28,[32][33][34]. In a general context, the relevant quantities in granular medium are located at the microscopic scale referred to the particles and contacts.…”

Section: Von-mises Stress Fieldmentioning

confidence: 99%

“…The third step consists in generating the heterogeneous material with several inclusions representing 85 % of the whole area. In the fourth step, emphasis is [25,26] and the spacetime analysis described by De-Saxcé et al [27,28]. Secondly, effective elastic properties are predicted considering tensile and shear tests, and compared to those obtained using other numerical methods.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of DEM to predict the elastic behavior of particulate composite materials

Haddad¹,

Leclerc²,

Guessasma³

et al. 2015

Granular Matter

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The present paper deals with a novel method to predict the effective elastic behavior of heterogeneous continuous materials using discrete element method. This work uses a numerical approach based on a hybrid particulatelattice model in which discrete elements are linked by cohesive forces through beam elements. Mechanical tests, carried out on particulate composite material, are performed in terms of effective elastic properties and stress fields which exhibit a good adequation with other numerical and analytical approaches such as the finite element method and the Fast Fourier Transform based method. As an example, the proposed approach is performed to predict the elastic properties of a ceramic/resin composite as well as the local effects by means of equivalent Von Mises stress.

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Section: Von-mises Stress Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of DEM to predict the elastic behavior of particulate composite materials

Haddad¹,

Leclerc²,

Guessasma³

et al. 2015

Granular Matter

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“…Also, an alternative expression for the effective stress tensor was included in Xie and Sha (2012) and Nicot et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic gradient-based poroplastic theory for concrete under high temperatures

Ripani

Etse

Vrech

et al. 2014

International Journal of Plasticity

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Concrete materials subjected to long term exposures to high temperatures suffer severe degradations in its mechanical properties (cohesion, friction, strength and stiffness) and changes in their failure mechanisms. These degradations may lead to irreversible damage or sudden collapse of the related structures. From the predictive analysis stand point, accurate constitutive theories are required to simulate the variations of concrete mechanical failure behavior under high and durable temperature fields. In the realm of the smeared crack approach, non-local model strategies are required to objectively reproduce failure behaviors under coupled thermo-mechanical loading conditions, while realistic descriptions of the involved characteristic lengths are needed to objectively reproduce the variation from ductile to brittle failure modes depending on the acting confining pressure and temperature. In this work, a thermodynamically consistent gradient poroplastic model for concrete subjected to high temperatures is proposed. A particular and simple form of gradient-based poroplasticity is considered whereby the state variables are the only ones of non-local character. The degradations of these variables due to coupled thermo-mechanical effects are described in the framework of the thermodynamic approach. After describing the material formulation, numerical analyses are presented which demonstrate the predictive capabilities of the proposed constitutive theory for different stress paths and thermal conditions.

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“…In response there has been a significant amount of recent work focused on developing consistent homogenisation processes that are applicable even in the absence of equilibrium. These approaches largely focus on calculating stress as an ensemble average of the stress within individual particles, defined from the point of view of the conservation of momentum at all points within a given particle (de Saxcé et al, 2004;Fortin et al, 2003;Fortin et al, 2002;Li et al, 2009;Nicot et al, 2013;Moreau, 2010;Luding, 2010). This work has shown that the components of stress arising from particle dynamics may be significant and are necessary for eliminating the asymmetry present in earlier quasi-static descriptions.…”

Section: Introductionmentioning

confidence: 99%

“…For the most part, the approach taken here is known (de Saxcé et al, 2004;Fortin et al, 2003;Fortin et al, 2002;Li et al, 2009;Nicot et al, 2013;Moreau, 2010; Luding, 2010), however we consider three-dimensions and arbitrary particle shape and progress to the point where a new interpretation can be made. In particular, we present an argument that the component of stress relating to the angular velocity of particles, often referred to as ''centrifugal stress' ' (de Saxcé et al, 2004;Nicot et al, 2013), be excluded without exception from the definition of bulk stress. Without this term, we make further observations on the nature of stress symmetry in granular materials that will greatly simplify the process of accounting for dynamics in certain classes of materials, including the vast majority of Discrete Element Models where spherical particles are still commonplace.…”

Section: Introductionmentioning

confidence: 99%

The effects of particle dynamics on the calculation of bulk stress in granular media

Smith

Wensrich

2014

International Journal of Solids and Structures

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a b s t r a c tExpressions for bulk stress within a granular material in a dynamic setting are reviewed and explicitly derived for assemblies of three dimensional arbitrary shaped particles. By employing classical continuum and rigid body mechanics, the mean stress tensor for a single particle is separated into three distinct components; the familiar Love-Webber formula describing the direct effect of contacts, a component due to the net unbalanced moment arising from contact and a symmetric term due to the centripetal acceleration of material within the particle. A case is made that the latter term be ignored without exception when determining bulk stress within an assembly of particles. In the absence of this centripetal term an important observation is made regarding the nature of the symmetry in the stress tensor for certain types of particles; in the case of particles with cubic symmetry, the effects of dynamics on the bulk stress in an assembly is captured by an entirely skew-symmetric tensor. In this situation, it is recognised that the symmetric part of the Love-Webber formula is all that is required for defining the mean stress tensor within an assembly -regardless of the dynamics of the system.

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On the definition of the stress tensor in granular media

Cited by 87 publications

References 15 publications

Application of DEM to predict the elastic behavior of particulate composite materials

Application of DEM to predict the elastic behavior of particulate composite materials

Thermodynamic gradient-based poroplastic theory for concrete under high temperatures

The effects of particle dynamics on the calculation of bulk stress in granular media

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