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http://hdl.handle.net/10985/10760
Proper Generalized Decomposition (PGD) for numerical calculation of polycrystalline aggregates under cyclic loading
NASRI, Mohamed Aziz; ROBERT, Camille; MOREL, Franck; EL AREM, Saber; AMMAR, Amine
none
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/107602015-01-01T00:00:00ZNASRI, Mohamed AzizROBERT, CamilleMOREL, FranckEL AREM, SaberAMMAR, AminenoneSimulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD)
http://hdl.handle.net/10985/10267
Simulation of Heat and Mass Transport in a Square Lid-Driven Cavity with Proper Generalized Decomposition (PGD)
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
The aim of this study is to apply proper generalized decomposition (PGD) to solve mixed-convection problems with and without mass transport in a two dimensional lid-driven cavity. PGD is an iterative reduced order model approach which consists of solving a partial differential equation while seeking the solution in separated form. Comparisons with results in the literature and with results from a standard solver are make. For the case of a mixed-convection problem without mass transfer, three Richardson numbers are considered, Ri=0.1, Ri=1, and Ri=10. In this case, PGD is seven times faster than the standard solver with Ri=10 with a similar accuracy. For the case with mass transfer, simulations are done with different Lewis numbers, Le=5, Le=25, and Le=50, and with different value of the ratio N between the solutal and the thermal Grashoff numbers. In this case, too, PGD is ten times faster than the standard solver.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102672013-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineThe aim of this study is to apply proper generalized decomposition (PGD) to solve mixed-convection problems with and without mass transport in a two dimensional lid-driven cavity. PGD is an iterative reduced order model approach which consists of solving a partial differential equation while seeking the solution in separated form. Comparisons with results in the literature and with results from a standard solver are make. For the case of a mixed-convection problem without mass transfer, three Richardson numbers are considered, Ri=0.1, Ri=1, and Ri=10. In this case, PGD is seven times faster than the standard solver with Ri=10 with a similar accuracy. For the case with mass transfer, simulations are done with different Lewis numbers, Le=5, Le=25, and Le=50, and with different value of the ratio N between the solutal and the thermal Grashoff numbers. In this case, too, PGD is ten times faster than the standard solver.The proper generalized decomposition for the simulation of delamination using cohesive zone model
http://hdl.handle.net/10985/8491
The proper generalized decomposition for the simulation of delamination using cohesive zone model
METOUI, Sondes; IORDANOFF, Ivan; DAU, Frédéric; PRULIERE, Etienne; AMMAR, Amine
The use of cohesive zone models is an efficient way to treat the damage, especially when the crack path is known a priori. This is the case in the modeling of delamination in composite laminates. However, the simulations using cohesive zone models are expensive in a computational point of view. When using implicit time integration scheme or when solving static problems, the non-linearity related to the cohesive model requires many iterations before reaching convergence. In explicit approaches, the time step stability condition also requires an important number of iterations. In this article, a new approach based on a separated representation of the solution is proposed. The Proper Generalized Decomposition is used to build the solution. This technique, coupled with a cohesive zone model, allows a significant reduction of the computational cost. The results approximated with the PGD are very close to the ones obtained using the classical finite element approach.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/84912014-01-01T00:00:00ZMETOUI, SondesIORDANOFF, IvanDAU, FrédéricPRULIERE, EtienneAMMAR, AmineThe use of cohesive zone models is an efficient way to treat the damage, especially when the crack path is known a priori. This is the case in the modeling of delamination in composite laminates. However, the simulations using cohesive zone models are expensive in a computational point of view. When using implicit time integration scheme or when solving static problems, the non-linearity related to the cohesive model requires many iterations before reaching convergence. In explicit approaches, the time step stability condition also requires an important number of iterations. In this article, a new approach based on a separated representation of the solution is proposed. The Proper Generalized Decomposition is used to build the solution. This technique, coupled with a cohesive zone model, allows a significant reduction of the computational cost. The results approximated with the PGD are very close to the ones obtained using the classical finite element approach.Numerical and Experimental Investigations on Deep Drawing of G1151 Carbon Fiber Woven Composites
http://hdl.handle.net/10985/11147
Numerical and Experimental Investigations on Deep Drawing of G1151 Carbon Fiber Woven Composites
GHERISSI, Abderraouf; ABBASSI, Fethi; ZGHAL, Ali; AMMAR, Amine
This study proposes to simulate the deep drawing on carbon woven composites in order to reduce the manufacturing cost and waste of composite material during the stamping process, The multi-scale anisotropic approach of woven composite was used to develop a finite element model for simulating the orientation of fibers accurately and predicting the deformation of composite during mechanical tests and forming process. The proposed experimental investigation for bias test and hemispherical deep drawing process is investigated in the G1151 Interlock. The mechanical properties of carbon fiber have great influence on the deformation of carbon fiber composites. In this study, shear angle–displacement curves and shear load–shear angle curves were obtained from a bias extension test. Deep drawing experiments and simulation were conducted, and the shear load–displacement curves under different forming depths and shear angle–displacement curves were obtained. The results showed that the compression and shear between fibers bundles were the main deformation mechanism of carbon fiber woven composite, as well as the maximum shear angle for the composites with G1151 woven fiber was 58°. In addition, during the drawing process, it has been found that the forming depth has a significant influence on the drawing force. It increases rapidly with the increasing of forming depth. In this approach the suitable forming depth deep drawing of the sheet carbon fiber woven composite was approximately 45 mm.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/111472016-01-01T00:00:00ZGHERISSI, AbderraoufABBASSI, FethiZGHAL, AliAMMAR, AmineThis study proposes to simulate the deep drawing on carbon woven composites in order to reduce the manufacturing cost and waste of composite material during the stamping process, The multi-scale anisotropic approach of woven composite was used to develop a finite element model for simulating the orientation of fibers accurately and predicting the deformation of composite during mechanical tests and forming process. The proposed experimental investigation for bias test and hemispherical deep drawing process is investigated in the G1151 Interlock. The mechanical properties of carbon fiber have great influence on the deformation of carbon fiber composites. In this study, shear angle–displacement curves and shear load–shear angle curves were obtained from a bias extension test. Deep drawing experiments and simulation were conducted, and the shear load–displacement curves under different forming depths and shear angle–displacement curves were obtained. The results showed that the compression and shear between fibers bundles were the main deformation mechanism of carbon fiber woven composite, as well as the maximum shear angle for the composites with G1151 woven fiber was 58°. In addition, during the drawing process, it has been found that the forming depth has a significant influence on the drawing force. It increases rapidly with the increasing of forming depth. In this approach the suitable forming depth deep drawing of the sheet carbon fiber woven composite was approximately 45 mm.Effect of the inverse Langevin approximation on the solution of the Fokker-Planck equation of non-linear dilute polymer
http://hdl.handle.net/10985/11141
Effect of the inverse Langevin approximation on the solution of the Fokker-Planck equation of non-linear dilute polymer
AMMAR, Amine
The Langevin function is defined by L (x ) = coth (x ) −1 /x . Its inverse is useful for many applications and especially for polymer science. As the inverse exact expression has no analytic representation, many ap- proximations have been established. The most famous approximation is the one traditionally used for the finitely extensible non-linear elastic (FENE) dumbbell model in which the inverse is approximated by L −1 (y ) = 3 y/ (1 −y 2 ) . Recently Martin Kröger has published a paper entitled ‘Simple, admissible and accurate approximations of the inverse Langevin and Brillouin functions, relevant for strong polymer de- formation and flows’ (Kröger, 2015) in which he proposed approximations with very reduced error in relation to the numeric inverse of the Langevin function. The question we aim to analyze in this short communication is: when one uses the traditional approximation rather than the more accurate one pro- posed by Kröger is that really significant regarding the value of the probability distribution function (PDF) in the frame work of a kinetic theory simulation? If yes when we move to the upper scale by evaluating the value of the stress, can we observe a significant difference? By making some simple 1D simulations in homogeneous extensional flow it is demonstrated in this short communication that the PDF prediction within kinetic theory framework as well as the macroscopic stress value are both affected by the quality of the approximation.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/111412016-01-01T00:00:00ZAMMAR, AmineThe Langevin function is defined by L (x ) = coth (x ) −1 /x . Its inverse is useful for many applications and especially for polymer science. As the inverse exact expression has no analytic representation, many ap- proximations have been established. The most famous approximation is the one traditionally used for the finitely extensible non-linear elastic (FENE) dumbbell model in which the inverse is approximated by L −1 (y ) = 3 y/ (1 −y 2 ) . Recently Martin Kröger has published a paper entitled ‘Simple, admissible and accurate approximations of the inverse Langevin and Brillouin functions, relevant for strong polymer de- formation and flows’ (Kröger, 2015) in which he proposed approximations with very reduced error in relation to the numeric inverse of the Langevin function. The question we aim to analyze in this short communication is: when one uses the traditional approximation rather than the more accurate one pro- posed by Kröger is that really significant regarding the value of the probability distribution function (PDF) in the frame work of a kinetic theory simulation? If yes when we move to the upper scale by evaluating the value of the stress, can we observe a significant difference? By making some simple 1D simulations in homogeneous extensional flow it is demonstrated in this short communication that the PDF prediction within kinetic theory framework as well as the macroscopic stress value are both affected by the quality of the approximation.Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
http://hdl.handle.net/10985/8469
Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/84692011-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineIn this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
http://hdl.handle.net/10985/8462
Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
BERGAMASCO, Luca; IZQUIERDO, Salvador; AMMAR, Amine
Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84622013-01-01T00:00:00ZBERGAMASCO, LucaIZQUIERDO, SalvadorAMMAR, AmineMicro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach.Réduction dimensionnelle de type PGD pour le calcul numérique d’agrégats polycristallin soumis à des chargements cycliques
http://hdl.handle.net/10985/10755
Réduction dimensionnelle de type PGD pour le calcul numérique d’agrégats polycristallin soumis à des chargements cycliques
NASRI, Mohamed Aziz; ROBERT, Camille; MOREL, Franck; EL AREM, Saber; AMMAR, Amine
Les modélisations numériques des matériaux à l’échelle de la microstructure se sont fortement développées au cours des deux dernières décennies. Malheureusement, les méthodes de résolution classiques ne permettent pas de simuler les agrégats polycristallins au-delà de quelques dizaines de cycles à cause du temps de calcul prohibitif. Ce travail présente le développement d’une méthode numérique pour la résolution par la méthode des éléments finis d’agrégats polycristallins soumis à un chargement cyclique. La première idée est de maintenir la matrice de rigidité constante. La deuxième proposition est d’utiliser une méthode de réduction dimensionnelle en espace/temps. Les résultats montrent un gain de temps relativement important tout en gardant une très bonne précision
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/107552015-01-01T00:00:00ZNASRI, Mohamed AzizROBERT, CamilleMOREL, FranckEL AREM, SaberAMMAR, AmineLes modélisations numériques des matériaux à l’échelle de la microstructure se sont fortement développées au cours des deux dernières décennies. Malheureusement, les méthodes de résolution classiques ne permettent pas de simuler les agrégats polycristallins au-delà de quelques dizaines de cycles à cause du temps de calcul prohibitif. Ce travail présente le développement d’une méthode numérique pour la résolution par la méthode des éléments finis d’agrégats polycristallins soumis à un chargement cyclique. La première idée est de maintenir la matrice de rigidité constante. La deuxième proposition est d’utiliser une méthode de réduction dimensionnelle en espace/temps. Les résultats montrent un gain de temps relativement important tout en gardant une très bonne précisionSpace–time proper generalized decompositions for the resolution of transient elastodynamic models
http://hdl.handle.net/10985/8461
Space–time proper generalized decompositions for the resolution of transient elastodynamic models
BOUCINHA, Lucas; GRAVOUIL, Anthony; AMMAR, Amine
In this paper, we investigate ability of proper generalized decomposition (PGD) to solve transient elastodynamic models in space–time domain. Classical methods use time integration schemes and an incremental resolution process. We propose here to use standard time integration methods in a non-incremental strategy. As a result, PGD gives a separated representation of the space–time solution as a sum of tensorial products of space and time vectors, that we interpret as space–time modes. Recent time integration schemes are based on multi-field formulations. In this case, separated representation can be constructed using state vectors in space and same vectors in time. However, we have experienced bad convergence order using this decomposition. Furthermore, temporal approximation must be the same for all fields. Thus, we propose an extension of classical separated representation for multi-field problems. This multi-field PGD (MF-PGD) uses space and time vectors that are different for each field. Calculation of decomposition is done using a monolithic approach in space and time, potentially allowing the use of different approximations in space and time. Finally, several simulations are performed with the transient elastodynamic problem with one dimension in space. Different approximations in time are investigated: Newmark scheme, single field time discontinuous Galerkin method and two fields time continuous and discontinuous Galerkin methods.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84612013-01-01T00:00:00ZBOUCINHA, LucasGRAVOUIL, AnthonyAMMAR, AmineIn this paper, we investigate ability of proper generalized decomposition (PGD) to solve transient elastodynamic models in space–time domain. Classical methods use time integration schemes and an incremental resolution process. We propose here to use standard time integration methods in a non-incremental strategy. As a result, PGD gives a separated representation of the space–time solution as a sum of tensorial products of space and time vectors, that we interpret as space–time modes. Recent time integration schemes are based on multi-field formulations. In this case, separated representation can be constructed using state vectors in space and same vectors in time. However, we have experienced bad convergence order using this decomposition. Furthermore, temporal approximation must be the same for all fields. Thus, we propose an extension of classical separated representation for multi-field problems. This multi-field PGD (MF-PGD) uses space and time vectors that are different for each field. Calculation of decomposition is done using a monolithic approach in space and time, potentially allowing the use of different approximations in space and time. Finally, several simulations are performed with the transient elastodynamic problem with one dimension in space. Different approximations in time are investigated: Newmark scheme, single field time discontinuous Galerkin method and two fields time continuous and discontinuous Galerkin methods.Proper Generalized Decomposition method for incompressible Navier–Stokes equations with a spectral discretization
http://hdl.handle.net/10985/8487
Proper Generalized Decomposition method for incompressible Navier–Stokes equations with a spectral discretization
DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
Proper Generalized Decomposition (PGD) is a method which consists in looking for the solution to a problem in a separate form. This approach has been increasingly used over the last few years to solve mathematical problems. The originality of this work consists in the association of PGD with a spectral collocation method to solve transfer equations as well as Navier–Stokes equations. In the first stage, the PGD method and its association with spectral discretization is detailed. This approach was tested for several problems: the Poisson equation, the Darcy problem, Navier–Stokes equations (the Taylor Green problem and the lid-driven cavity). In the Navier–Stokes problems, the coupling between velocity and pressure was performed using a fractional step scheme and a PN—PN-2 discretization. For all problems considered, the results from PGD simulations were compared with those obtained by a standard solver and/or with the results found in the literature. The simulations performed showed that PGD is as accurate as standard solvers. PGD preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases. Moreover, for a given number of discretization nodes, PGD is faster than the standard solvers.
http://dx.doi.org/10.1016/j.amc.2013.02.022
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84872013-01-01T00:00:00ZDUMON, AntoineALLERY, CyrilleAMMAR, AmineProper Generalized Decomposition (PGD) is a method which consists in looking for the solution to a problem in a separate form. This approach has been increasingly used over the last few years to solve mathematical problems. The originality of this work consists in the association of PGD with a spectral collocation method to solve transfer equations as well as Navier–Stokes equations. In the first stage, the PGD method and its association with spectral discretization is detailed. This approach was tested for several problems: the Poisson equation, the Darcy problem, Navier–Stokes equations (the Taylor Green problem and the lid-driven cavity). In the Navier–Stokes problems, the coupling between velocity and pressure was performed using a fractional step scheme and a PN—PN-2 discretization. For all problems considered, the results from PGD simulations were compared with those obtained by a standard solver and/or with the results found in the literature. The simulations performed showed that PGD is as accurate as standard solvers. PGD preserves the spectral behavior of the errors in velocity and pressure when the time step or the space step decreases. Moreover, for a given number of discretization nodes, PGD is faster than the standard solvers.