Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
9
1
2011
SPECIAL ISSUE Recent Advances in the Multiscale Modeling and Simulation of Complex Fluids
F.
Chinesta
EADS Corporate International Chair, Ecole Centrale de Nantes, 1 rue de la Noe, 44321 Nantes Cedex 3, France
Elias
Cueto
Group of Structural Mechanics and Materials Modelling (GEMM), Aragon Institute of Engineering Research (I3A), Betancourt Building, Maria de Luna, 5, E-50018 Zaragoza, Spain
vii-viii
MESHLESS STOCHASTIC SIMULATION OF MICRO-MACROKINETIC THEORY MODELS
We present in this paper a numerical technique for the stochastic simulation of molecular models of viscoelastic fluids based on kinetic theory. The technique is based on the use of meshless methods and allows for an updated Lagrangian description of the conservation equations. It makes use of natural neighbor Galerkin schemes that allow for a proper geometrical description of the domain as it evolves. The presented technique is especially well suited for the numerical simulation of free-surface flows. In this way, model molecules are associated with nodal positions such that they are advected with material velocities. Problems associated with lack of molecules in certain elements, for instance, as encountered in the basic implementation of CONNFFESSIT approaches, are thus avoided. We present examples of validation and also performance tests of this technique applied to finite extension nonlinear elastic (FENE) and reptation (Doi-Edwards) models.
Elias
Cueto
Group of Structural Mechanics and Materials Modelling (GEMM), Aragon Institute of Engineering Research (I3A), Betancourt Building, Maria de Luna, 5, E-50018 Zaragoza, Spain
M.
Laso
Laboratory of Non-Metallic Materials, Department of Chemical Engineering, Universidad Poliecnica de Madrid, Jose Gutierrez Abascal 2, E-28006 Madrid, Spain
F.
Chinesta
EADS Corporate International Chair, Ecole Centrale de Nantes, 1 rue de la Noe, 44321 Nantes Cedex 3, France
1-16
COUPLING FINITE ELEMENTS AND PROPER GENERALIZED DECOMPOSITIONS
Numerous models encountered in science and engineering exist, despite the impressive recent progresses attained in computational simulation techniques, intractable when the usual and experienced discretization techniques are applied for their numerical simulation. Thus, different challenging issues remain for the proposal of new alternative advanced simulation techniques. Separated representations offer the possibility to address some challenging models with CPU time savings of some orders of magnitude. In other cases, they allowed models to be addressed which until now, have never been solved. The number of published works concerning this kind of approximation remains quite reduced, and then numerous difficulties that were successfully circumvented in the context of more experienced discretization techniques, as is the case of the finite element method, must be considered again within the separated representation framework. One of these issues in the one that concerns the treatment of localized behavior of model solutions. This work focuses on this topic and proposes an efficient finite element (or extended finite element) enrichment of usual separated representation.
A.
Ammar
Arts et Metiers Paris Tech 2 Boulevard du Ronceray, BP 93525, F-49035 Angers Cedex 01, France
F.
Chinesta
EADS Corporate Foundation International Chair, GeM: UMR CNRS-Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, F-44321 Nantes Cedex 3, France
Elias
Cueto
Group of Structural Mechanics and Materials Modelling (GEMM), Aragon Institute of Engineering Research (I3A), Betancourt Building, Maria de Luna, 5, E-50018 Zaragoza, Spain
17-33
THERMODYNAMICS: A STRUCTURE EMERGING IN THESTUDY OF RELATIONS AMONG DIFFERENT SCALES
Separation of scales becomes problematic in complex fluids. Some sort of multiscale analysis is inevitable. We show that a sufficiently general formulation of thermodynamics provides a unified framework for such analysis. Among the illustrations of the framework, we develop a basis for (i) an extension of the Simha-Somcynski equilibrium theory of polymeric fluids to a rheological theory and (ii) a new approach to the formulation of governing equations of direct molecular simulations of fluids subjected to flow and temperature gradients.
F.
Chinesta
EADS Corporate International Chair, Ecole Centrale de Nantes, 1 rue de la Noe, 44321 Nantes Cedex 3, France
Miroslav
Grmela
Ecole Polytechnique de Montreal, C.P. 6079 suc. Centre-ville, Montreal, H3C 3A7, Quebec, Canada
35-51
ULTRASONIC WELDING OF THERMOPLASTIC COMPOSITES: MODELING OF THE PROCESS USING TIME HOMOGENIZATION
The process of ultrasonic welding allows assembly of thermoplastic composite parts. A high-frequency vibration imposed
to the processing zone induces self-heating and melting of the polymer. The main feature of this process is the existence
of phenomena that occur on two very different time scales: the vibration (about 10-5 s) and the flow of molten polymer
(about 1 s). In order to accurately simulate these phenomena without the use of a very fine time discretization over
the whole process, we apply a time homogenization technique. First, the thermomechanical problem is formulated
using a Maxwell viscoelastic constitutive law, and then it is homogenized using asymptotic expansion. This leads
to three coupled problems: a microchronological mechanical problem, a macrochronological mechanical problem, and
a macrochronological thermal problem. This coupled formulation is actually simpler because the macrochronological
problems do not depend on the micro time scale and its associated fast variations. Lastly, a uniform simple test case
is proposed to compare the homogenized solution to a direct calculation. It shows that the method gives good results,
provided that the vibration is fast enough compared to the duration of the process. Moreover, the time savings appears
to be highly reduced, to 1,000 times less.
Arthur
Levy
GeM - Ecole Centrale Nantes, Universite de Nantes - 1 rue de la Noe 44321 Nantes, France
Steven
Le Corre
GeM - Ecole Centrale Nantes, Universite de Nantes - 1 rue de la Noe 44321 Nantes, France
Arnaud
Poitou
GeM - Ecole Centrale Nantes, Universite de Nantes - 1 rue de la Noe 44321 Nantes, France
Eric
Soccard
EADS IW - Technocampus, 1 rue de la Noe 44321 Nantes, France
53-72
THE PREDICTION OF PLANE COUETTE FLOW FOR A FENEFLUID USING A REDUCED BASIS APPROXIMATION OF THE FOKKER-PLANCK EQUATION
The start-up of plane Couette flow of a finitely extensible nonlinear elastic (FENE) fluid is considered. A numerical method for solving this problem based on a decoupled micro{macro approach is described. The polymeric stress is determined in the microscopic part of the calculation by computing the solution of a Fokker-Planck equation for the configuration probability density function. The solution of this equation often suffers from the so-called problem of "curse of dimensionality." An efficient solution procedure is described based on the use of an adaptive reduced basis function technique in conjunction with high-order spectral approximations. A substantial reduction in the number of degrees of freedom to achieve a required level of accuracy is obtained compared with standard tensor product representation of the basis. Some sample numerical results are presented to highlight properties of the model and the numerical scheme.
G. M.
Leonenko
School of Mathematics, Cardiff University, Cardiff, CF24 4AG, United Kingdom
T. N.
Phillips
School of Mathematics, Cardiff University, Cardiff, CF24 4AG, United Kingdom
73-88
IMPROVING THE ACCURACY OF LATTICE BOLTZMANN SIMULATIONS OF LIQUID MICROFLOWS
The simulation of incompressible flows at very low Reynolds numbers (Stokes regime) with the standard lattice Boltzmann method (collision-propagation algorithm) is hindered by a limitation of accuracy due to the relationship between viscosity and the Mach and Reynolds numbers. We present a multirelaxation-time lattice-Boltzmann method with modified equilibrium moments that allows improvement of accuracy for a given resolution at very low-Reynolds-number flows. This is paramount for liquid microflow simulations and for multiscale coupling in many practical instances, such as when the fluid motion is highly influenced by bounding or particulate immersed solids. The method as presented is restricted to steady-state flows, which include many fluid-flow applications at the microscale. The viscous flow with slip of a liquid in a long microchannel, for which an analytical solution exists, has been used as the test case.
Salvador
Izquierdo
Fluid Mechanics Group, University of Zaragoza and LITEC (CSIC), Maria de Luna 3, 50018, Zaragoza, Spain
Norberto
Fueyo
Fluid Mechanics Group, University of Zaragoza, and LITEC (CSIC), Spain
89-96
DERIVATION OF THE YOUNG'S AND SHEAR MODULI OFSINGLE-WALLED CARBON NANOTUBES THROUGH A COMPUTATIONAL HOMOGENIZATION APPROACH
In this study, the computation of the traction-torsion-bending behavior of single-walled carbon nanotubes (SWCNTs) is investigated. A structural mechanics model is used to describe the response of the nanotube; the atomic interactions are represented with 3D beams. Nanotubes are slender structures, taking benefit from their axial periodicity or helical symmetry. Homogenization theory is used to obtain their overall beam behavior from the solution of basic cell problems. These problems are solved through a finite element approach and involve concise models, whatever the SWCNT type. The computed results show that the bending behavior appears to be decoupled from the axial one and independent of the moment direction. Young's and shear moduli are derived, and it is shown that the Young's moduli are very close in traction and bending. Comparisons with the data in the literature reveal good agreements. Finally, scale effects are studied, and the moduli of the SWCNTs are compared to those of the graphene, thus demonstrating mechanical sensitivity to curvature.
Elie
El Khoury
Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Ecole Centrale deNantes, BP 92101, 44321, Nantes Cedex 3, France
Tanguy
Messager
Laboratoire de Mecanique de Lille (UMR CNRS 8107), Universite Lille 1, Cite Scientifique, 59655 Villeneuve d'Ascq Cedex, France
Patrice
Cartraud
Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Ecole Centrale deNantes, BP 92101, 44321, Nantes Cedex 3, France
97-118
MOLECULAR DYNAMICS PREDICTION OF ELASTICAND PLASTIC DEFORMATION OF SEMICRYSTALLINE POLYETHYLENE
The elastic and large plastic deformations of semicrystalline polymers involve the multiscale organization of molecules inside spherulites and depend on the deformation path. Under a tensile test, as an effect of the lamellar organization, the first steps of elastic-plastic deformation are localized in a very thin layer in the equatorial zone, as shown by experiments. The molecular mechanism and the resulting stress{strain properties can be predicted by molecular dynamics simulations. An all-atom model is necessary to predict the behavior of polyethylene chains inside the amorphous and crystalline phases. Two large-molecular-weight polyethylene chains with a complex path are involved in crystalline and amorphous phases and in their interconnection with a 3D periodic condition. This paper explains the main physical characteristics of semicrystalline organization and the building process of this first molecular model which is fully coupled. This model, stretched along the thickness of the lamellae, is representative of the equatorial zone in a spherulite during the first steps of elastic and plastic deformation. The deformation mechanism of amorphous and crystalline phases is analyzed as a function of strain and strain-rate. A nanocavitation in the amorphous phase results from a topological constraint imposed by the crystalline phase. This mechanism is a natural consequence of the model and explains the cavitation observed at a macroscopic level.
Severine
Queyroy
CEMEF, ENSMP, 1 rue Claude Daunesse F-06940 Sophia Antipolis, France
Bernard
Monasse
CEMEF, ENSMP, 1 rue Claude Daunesse F-06940 Sophia Antipolis, France
119-136