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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.Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers
http://hdl.handle.net/10985/6595
Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers
PRULIERE, Etienne; AMMAR, Amine; EL KISSI, Nadia; CHINESTA, Francisco
Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic advection equations. In non-recirculating flows, Eulerian discretizations can give a convergent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In this paper we compares different advanced strategies (some of them recently proposed and extended here for addressing complex flows) when they are applied to the solution of the kinetic theory description of a short fiber suspension fluid flows.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/65952009-01-01T00:00:00ZPRULIERE, EtienneAMMAR, AmineEL KISSI, NadiaCHINESTA, FranciscoNumerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic advection equations. In non-recirculating flows, Eulerian discretizations can give a convergent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In this paper we compares different advanced strategies (some of them recently proposed and extended here for addressing complex flows) when they are applied to the solution of the kinetic theory description of a short fiber suspension fluid flows.On the space-time separated representation of integral linear viscoelastic models
http://hdl.handle.net/10985/9958
On the space-time separated representation of integral linear viscoelastic models; Représentation séparée espace-temps pour des comportements viscoélastiques linaires intégraux
AMMAR, Amine; ZGHAL, Ali; MOREL, Franck; CHINESTA, Francisco
The analysis of materials mechanical behavior involves many computational challenges. In this work, we are addressing the transient simulation of the mechanical behavior when the time of interest is much larger than the characteristic time of the mechanical response. This situation is encountered in many applications, as for example in the simulation of materials aging, or in structural analysis when small-amplitude oscillatory loads are applied during a long period, as it occurs for example when characterizing viscoelastic behaviors by calculating the complex modulus or when addressing fatigue simulations. Moreover, in the case of viscoelastic behaviors, the constitutive equation is many times expressed in an integral form avoiding the necessity of using internal variables, fact that results in an integro-differential model. In order to efficiently simulate such a model, we explore in this work the use of a space-time separated representation.; L'analyse du comportement mécanique des matériaux entraîne de nombreuses difficultés du point de vue numérique. Dans ce travail, nous allons nous focaliser sur l'une d'entre elles, celle associée à la simulation transitoire du comportement mécanique quand l'intervalle temporel d'intérêt est substantiellement plus long que le temps caractéristique associé à la réponse mécanique. Cette situation est fréquemment retrouvée dans la caractérisation rhéologique des matériaux viscoélastiques (pour la détermination du module complexe) ainsi que quand on s'attaque à la simulation de la fatigue. De plus, dans le cas des matriaux viscoélastiques, le comportement est généralement décrit par une loi de comportement intégrale qui évite le besoin d'utiliser des variables internes, donnant lieu à un modèle mécanique integro-différentiel. Pour une résolution efficace, nous analysons ici l'utilisation d'une représentation séparée en espace-temps.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/99582015-01-01T00:00:00ZAMMAR, AmineZGHAL, AliMOREL, FranckCHINESTA, FranciscoThe analysis of materials mechanical behavior involves many computational challenges. In this work, we are addressing the transient simulation of the mechanical behavior when the time of interest is much larger than the characteristic time of the mechanical response. This situation is encountered in many applications, as for example in the simulation of materials aging, or in structural analysis when small-amplitude oscillatory loads are applied during a long period, as it occurs for example when characterizing viscoelastic behaviors by calculating the complex modulus or when addressing fatigue simulations. Moreover, in the case of viscoelastic behaviors, the constitutive equation is many times expressed in an integral form avoiding the necessity of using internal variables, fact that results in an integro-differential model. In order to efficiently simulate such a model, we explore in this work the use of a space-time separated representation.
L'analyse du comportement mécanique des matériaux entraîne de nombreuses difficultés du point de vue numérique. Dans ce travail, nous allons nous focaliser sur l'une d'entre elles, celle associée à la simulation transitoire du comportement mécanique quand l'intervalle temporel d'intérêt est substantiellement plus long que le temps caractéristique associé à la réponse mécanique. Cette situation est fréquemment retrouvée dans la caractérisation rhéologique des matériaux viscoélastiques (pour la détermination du module complexe) ainsi que quand on s'attaque à la simulation de la fatigue. De plus, dans le cas des matriaux viscoélastiques, le comportement est généralement décrit par une loi de comportement intégrale qui évite le besoin d'utiliser des variables internes, donnant lieu à un modèle mécanique integro-différentiel. Pour une résolution efficace, nous analysons ici l'utilisation d'une représentation séparée en espace-temps.Separated representation of incremental elastoplastic simulations
http://hdl.handle.net/10985/9514
Separated representation of incremental elastoplastic simulations
NASRI, Mohamed Aziz; AGUADO, Jose Vicente; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco; MOREL, Franck; ROBERT, Camille; EL AREM, Saber
Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/95142015-01-01T00:00:00ZNASRI, Mohamed AzizAGUADO, Jose VicenteAMMAR, AmineCUETO, EliasCHINESTA, FranciscoMOREL, FranckROBERT, CamilleEL AREM, SaberForming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.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; AMMAR, Amine; ZGHAL, Ali
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, FethiAMMAR, AmineZGHAL, AliThis 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.Kinetic Theory Microstructure Modeling in Concentrated Suspensions
http://hdl.handle.net/10985/10264
Kinetic Theory Microstructure Modeling in Concentrated Suspensions
ABISSET-CHAVANNE, Emmanuelle; MEZHER, Rabih; LE CORRE, Steven; AMMAR, Amine; CHINESTA, Francisco
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102642013-01-01T00:00:00ZABISSET-CHAVANNE, EmmanuelleMEZHER, RabihLE CORRE, StevenAMMAR, AmineCHINESTA, FranciscoWhen 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.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; PRULIERE, Etienne; AMMAR, Amine; DAU, Frédéric; IORDANOFF, Ivan
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, SondesPRULIERE, EtienneAMMAR, AmineDAU, FrédéricIORDANOFF, IvanThe 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.PGD-Based Computational Vademecum for Efficient Design, Optimization and Control
http://hdl.handle.net/10985/10241
PGD-Based Computational Vademecum for Efficient Design, Optimization and Control
CHINESTA, Francisco; LEYGUE, Adrien; BORDEU, Felipe; AGUADO, Jose Vicente; CUETO, Elias; GONZALEZ, David; ALFARO, Iciar; AMMAR, Amine; HUERTA, Antonio
In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102412013-01-01T00:00:00ZCHINESTA, FranciscoLEYGUE, AdrienBORDEU, FelipeAGUADO, Jose VicenteCUETO, EliasGONZALEZ, DavidALFARO, IciarAMMAR, AmineHUERTA, AntonioIn this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.Nonincremental proper generalized decomposition solution of parametric uncoupled models defined in evolving domains
http://hdl.handle.net/10985/10287
Nonincremental proper generalized decomposition solution of parametric uncoupled models defined in evolving domains
AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
This work addresses the recurrent issue related to the existence of reduced bases related to the solution of parametric models defined in evolving domains. In this first part of the work, we address the case of decoupled kinematics, that is, models whose solution does not affect the domain in which they are defined. The chosen framework considers an updated Lagrangian description of the kinematics, solved by using natural neighbor Galerkin methods within a nonincremental space–time framework that can be generalized for addressing parametric models. Examples showing the performance and potentialities of the proposed methodology are included.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/102872012-01-01T00:00:00ZAMMAR, AmineCUETO, EliasCHINESTA, FranciscoThis work addresses the recurrent issue related to the existence of reduced bases related to the solution of parametric models defined in evolving domains. In this first part of the work, we address the case of decoupled kinematics, that is, models whose solution does not affect the domain in which they are defined. The chosen framework considers an updated Lagrangian description of the kinematics, solved by using natural neighbor Galerkin methods within a nonincremental space–time framework that can be generalized for addressing parametric models. Examples showing the performance and potentialities of the proposed methodology are included.Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices
http://hdl.handle.net/10985/10254
Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices
ALFARO, Iciar; GONZALEZ, David; BORDEU, Felipe; LEYGUE, Adrien; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
Simulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/102542014-01-01T00:00:00ZALFARO, IciarGONZALEZ, DavidBORDEU, FelipeLEYGUE, AdrienAMMAR, AmineCUETO, EliasCHINESTA, FranciscoSimulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.