Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

Prulière, Etienne; Ammar, Amine; Kissi, Nadia El; Chinesta, Francisco

doi:10.1007/s11831-008-9027-9

Cited by 48 publications

(41 citation statements)

References 44 publications

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“…Thus, an approximate closure relation is needed in order to express the fourth-order moment A as a function of the lower-order moment a. Different closure relations have been introduced and widely used [2] [10] [19] [25]. In what follows we consider the hybrid closure relation, that constitutes a good compromise between implementation simplicity and solution accuracy.…”

Section: Revisiting Jeffery's Modelmentioning

confidence: 99%

On the role of standard and anomalous diffusion in suspensions of rigid rods

Nadal¹,

Aguado²,

Abisset-Chavanne³

et al. 2015

Proceedings of 2nd International Electronic Conference on Entropy and Its Applications

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Dilute suspensions composed of rods are usually described by using the Jeffery's model that only considers flow-induced orientation. When the concentration increases rods interaction cannot be neglected and the simplest way to take it into account is from a diffusion term that tends to recover an isotropic orientation distribution. However, when considering CNTs suspensions involving large interaction networks, fractional diffusion better describes linear viscoelastic tests. In this work we revisit the fractional diffusion model analyzing its behaviour when applied in nonlinear regimes.

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Section: Revisiting Jeffery's Modelmentioning

confidence: 99%

On the role of standard and anomalous diffusion in suspensions of rigid rods

Nadal¹,

Aguado²,

Abisset-Chavanne³

et al. 2015

Proceedings of 2nd International Electronic Conference on Entropy and Its Applications

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“…To determine F Nþ1 and G Nþ1 a non-linear problem has to be solved. An alternate directions strategy has given excellent results in our precedent studies (for example in [15]). This method is performed in two steps:…”

Section: Enriching the Approximation Basismentioning

confidence: 99%

3D simulation of laminated shell structures using the Proper Generalized Decomposition

Prulière¹

2014

Composite Structures

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Numerical simulations of composite structures are generally performed using multi-layered shell elements in the context of the finite elements method. This strategy has numerous advantages like a low computation time and the capability to reproduce the comportment of composites in most of cases.The main restriction of this approach is that they require an approximation of the comportment in the thickness. This approximation is generally no more valid near the boundary and loading conditions and when non linear phenomena like delamination occurs in the thickness. This paper explores an alternative to shell computation using the framework of the Proper Generalized Decomposition that is based on a separated representation of the solution. The idea is to solve the full 3D solid problem separating the in-plane and the out-of-plane spaces. Practically, a classical shell mesh is used to describe the in-plane geometry and a simple 1D mesh is used to deal with the out-of-plane space. This allows to represents complex fields in the thickness without the complexity and the computation cost of a solid mesh which is particularly interesting when dealing with composite laminates.

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“…Usually, the fourth order moment, A, is expressed from the second order one by considering any of the numerous closure relations proposed in the literature [31][32][33][34]. We do not address this issue here, and from now on, we consider that A = L(a), with L, an appropriate algebraic operator.…”

Section: Micro-mechanical Description Of the Kinematics Of Deformablementioning

confidence: 99%

Kinetic Theory Microstructure Modeling in Concentrated Suspensions

Abisset-Chavanne

Mezher

Corre

et al. 2013

Entropy

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When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper.

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Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

Cited by 48 publications

References 44 publications

On the role of standard and anomalous diffusion in suspensions of rigid rods

On the role of standard and anomalous diffusion in suspensions of rigid rods

3D simulation of laminated shell structures using the Proper Generalized Decomposition

Kinetic Theory Microstructure Modeling in Concentrated Suspensions

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