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http://hdl.handle.net/10985/6477
Some Incipient Techniques For Improving Efficiency in Computational Mechanics
AMMAR, Amine; CHINESTA, Francisco
This contribution presents a review of different techniques available for alleviating simulation cost in computational mechanics. The first one is based on a separated representation of the unknown fields; the second one uses a model reduction based on the Karhunen-Loève decomposition within an adaptive scheme, and the last one is a mixed technique specially adapted for reducing models involving local singularities. These techniques can be applied in a large variety of models.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/64772008-01-01T00:00:00ZAMMAR, AmineCHINESTA, FranciscoThis contribution presents a review of different techniques available for alleviating simulation cost in computational mechanics. The first one is based on a separated representation of the unknown fields; the second one uses a model reduction based on the Karhunen-Loève decomposition within an adaptive scheme, and the last one is a mixed technique specially adapted for reducing models involving local singularities. These techniques can be applied in a large variety of models.Natural Element Method for the Simulation of Structures and Processes
http://hdl.handle.net/10985/9957
Natural Element Method for the Simulation of Structures and Processes
CHINESTA, Francisco; CESCOTTO, Serge; CUETO, Elias; LORONG, Philippe
The Natural Element Method (NEM) is halfway between meshless methods and the finite element method. This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material-forming processes involving solids and Newtonian and non-Newtonian fluids. The purpose of this text is to describe the natural element technique in its context, i.e. compared to the finite element-type techniques, which have proved reliable for many years, but also compared to other techniques with and without meshes. Both advantages and disadvantages of the technique have been listed. It has been written with a teaching purpose in mind, to be used by both professionals and students at Master's level.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/99572011-01-01T00:00:00ZCHINESTA, FranciscoCESCOTTO, SergeCUETO, EliasLORONG, PhilippeThe Natural Element Method (NEM) is halfway between meshless methods and the finite element method. This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material-forming processes involving solids and Newtonian and non-Newtonian fluids. The purpose of this text is to describe the natural element technique in its context, i.e. compared to the finite element-type techniques, which have proved reliable for many years, but also compared to other techniques with and without meshes. Both advantages and disadvantages of the technique have been listed. It has been written with a teaching purpose in mind, to be used by both professionals and students at Master's level.Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology
http://hdl.handle.net/10985/9991
Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology
CRUZ, Camilo; CHINESTA, Francisco; REGNIER, Gilles
Kinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/99912012-01-01T00:00:00ZCRUZ, CamiloCHINESTA, FranciscoREGNIER, GillesKinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks.On the solution of the multidimensional Langer’s equation using the proper generalized decomposition method for modeling phase transitions
http://hdl.handle.net/10985/8479
On the solution of the multidimensional Langer’s equation using the proper generalized decomposition method for modeling phase transitions
LAMARI, Hajer; AMMAR, Amine; LEYGUE, Adrien; CHINESTA, Francisco
The dynamics of phase transition in a binary mixture occurring during a quench is studied taking into account composition fluctuations by solving Langer’s equation in a domain composed of a certain number of micro-domains. The resulting Langer’s equation governing the evolution of the distribution function becomes multidimensional. Circumventing the curse of dimensionality the proper generalized decomposition is applied. The influence of the interaction parameter in the vicinity of the critical point is analyzed. First we address the case of a system composed of a single micro-domain in which phase transition occurs by a simple symmetry change. Next, we consider a system composed of two micro-domains in which phase transition occurs by phase separation, with special emphasis on the effect of the Landau free energy non-local term. Finally, some systems consisting of many micro-domains are considered.
http://dx.doi.org/10.1088/0965-0393/20/1/015007
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84792012-01-01T00:00:00ZLAMARI, HajerAMMAR, AmineLEYGUE, AdrienCHINESTA, FranciscoThe dynamics of phase transition in a binary mixture occurring during a quench is studied taking into account composition fluctuations by solving Langer’s equation in a domain composed of a certain number of micro-domains. The resulting Langer’s equation governing the evolution of the distribution function becomes multidimensional. Circumventing the curse of dimensionality the proper generalized decomposition is applied. The influence of the interaction parameter in the vicinity of the critical point is analyzed. First we address the case of a system composed of a single micro-domain in which phase transition occurs by a simple symmetry change. Next, we consider a system composed of two micro-domains in which phase transition occurs by phase separation, with special emphasis on the effect of the Landau free energy non-local term. Finally, some systems consisting of many micro-domains are considered.Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
http://hdl.handle.net/10985/8467
Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions
AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco
The numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/84672012-01-01T00:00:00ZAMMAR, AmineCUETO, EliasCHINESTA, FranciscoThe numerical solution of the chemical master equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task owing to its complexity, exponentially growing with the number of species involved. Although most of the existing techniques rely on the use of Monte Carlo-like techniques, we present here a new technique based on the approximation of the unknown variable (the probability of having a particular chemical state) in terms of a finite sum of separable functions. In this framework, the complexity of the CME grows only linearly with the number of state space dimensions. This technique generalizes the so-called Hartree approximation, by using terms as needed in the finite sums decomposition for ensuring convergence. But noteworthy, the ease of the approximation allows for an easy treatment of unknown parameters (as is frequently the case when modeling gene regulatory networks, for instance). These unknown parameters can be considered as new space dimensions. In this way, the proposed method provides solutions for any value of the unknown parameters (within some interval of arbitrary size) in one execution of the program.Flow modelling of quasi-Newtonian fluids in two-scale fibrous fabrics: Advanced simulations
http://hdl.handle.net/10985/11390
Flow modelling of quasi-Newtonian fluids in two-scale fibrous fabrics: Advanced simulations
AMMAR, Amine; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco; KEUNINGS, Roland
Permeability is the fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. In a previous work, the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and generalized Newtonian (shear-thinning) resins. In the linear case, only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as there are representative microscopic volumes in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, a large number of microscopic calculations must be carried out as the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. An original and efficient offline-online procedure was proposed for the solution of non-linear flow problems related to generalized Newtonian fluids in porous media. In this paper, this procedure is generalized to quasi-Newtonian fluids in order to evaluate the effect of extensional viscosity on the resulting upscaled permeability. This work constitutes a natural step forward in the definition of equivalent saturated permeabilities for linear and non-linear fluids.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/113902016-01-01T00:00:00ZAMMAR, AmineABISSET-CHAVANNE, EmmanuelleCHINESTA, FranciscoKEUNINGS, RolandPermeability is the fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. In a previous work, the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and generalized Newtonian (shear-thinning) resins. In the linear case, only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as there are representative microscopic volumes in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, a large number of microscopic calculations must be carried out as the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. An original and efficient offline-online procedure was proposed for the solution of non-linear flow problems related to generalized Newtonian fluids in porous media. In this paper, this procedure is generalized to quasi-Newtonian fluids in order to evaluate the effect of extensional viscosity on the resulting upscaled permeability. This work constitutes a natural step forward in the definition of equivalent saturated permeabilities for linear and non-linear fluids.Wavelet-based multiscale proper generalized decomposition
http://hdl.handle.net/10985/13282
Wavelet-based multiscale proper generalized decomposition
ANGEL, Leon; BARASINSKI, Anais; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco
Separated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132822018-01-01T00:00:00ZANGEL, LeonBARASINSKI, AnaisABISSET-CHAVANNE, EmmanuelleCUETO, EliasCHINESTA, FranciscoSeparated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear multi-scale character. In order to recover a multi-scale description of the solution within a separated representation framework, we study the use of wavelets for approximating the functions involved in the separated representation of the solution. We will prove that such an approach allows separating the different scales as well as taking profit from its multi-resolution behavior for defining adaptive strategies.Microscopic modelling of orientation kinematics of non-spherical particles suspended in confined flows using unilateral mechanics
http://hdl.handle.net/10985/13304
Microscopic modelling of orientation kinematics of non-spherical particles suspended in confined flows using unilateral mechanics
SCHEUER, Adrien; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco; KEUNINGS, Roland
The properties of reinforced polymers strongly depend on the microstructural state, that is, the orientation state of the fibres suspended in the polymeric matrix, induced by the forming process. Understanding flow-induced anisotropy is thus a key element to optimize both materials and process. Despite the important progresses accomplished in the modelling and simulation of suspensions, few works addressed the fact that usual processing flows evolve in confined configurations, where particles characteristic lengths may be greater than the thickness of the narrow gaps in which the flow takes place. In those circumstances, orientation kinematics models proposed for unconfined flows must be extended to the confined case. In this short communication, we propose an alternative modelling framework based on the use of unilateral mechanics, consequently exhibiting a clear analogy with plasticity and contact mechanics. This framework allows us to revisit the motion of confined particles in Newtonian and non-Newtonian matrices. We also prove that the confined kinematics provided by this model are identical to those derived from microstructural approaches
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/133042018-01-01T00:00:00ZSCHEUER, AdrienABISSET-CHAVANNE, EmmanuelleCHINESTA, FranciscoKEUNINGS, RolandThe properties of reinforced polymers strongly depend on the microstructural state, that is, the orientation state of the fibres suspended in the polymeric matrix, induced by the forming process. Understanding flow-induced anisotropy is thus a key element to optimize both materials and process. Despite the important progresses accomplished in the modelling and simulation of suspensions, few works addressed the fact that usual processing flows evolve in confined configurations, where particles characteristic lengths may be greater than the thickness of the narrow gaps in which the flow takes place. In those circumstances, orientation kinematics models proposed for unconfined flows must be extended to the confined case. In this short communication, we propose an alternative modelling framework based on the use of unilateral mechanics, consequently exhibiting a clear analogy with plasticity and contact mechanics. This framework allows us to revisit the motion of confined particles in Newtonian and non-Newtonian matrices. We also prove that the confined kinematics provided by this model are identical to those derived from microstructural approachesAdvanced parametric space-frequency separated representations in structural dynamics: A harmonic–modal hybrid approach
http://hdl.handle.net/10985/13277
Advanced parametric space-frequency separated representations in structural dynamics: A harmonic–modal hybrid approach
MUHAMMAD HARIS, Malik; BORZACCHIELLO, Domenico; AGUADO, Jose Vicente; CHINESTA, Francisco
This paper is concerned with the solution to structural dynamics equations. The technique here presented is closely related to Harmonic Analysis, and therefore it is only concerned with the long-term forced response. Proper Generalized Decomposition (PGD) is used to compute space-frequency separated representations by considering the frequency as an extra coordinate. This formulation constitutes an alternative to classical methods such as Modal Analysis and it is especially advantageous when parametrized structural dynamics equations are of interest. In such case, there is no need to solve the parametrized eigenvalue problem and the space-time solution can be recovered with a Fourier inverse transform. The PGD solution is valid for any forcing term that can be written as a combination of the considered frequencies. Finally, the solution is available for any value of the parameter. When the problem involves frequency-dependent parameters the proposed technique provides a specially suitable method that becomes computationally more efficient when it is combined with a modal representation.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132772018-01-01T00:00:00ZMUHAMMAD HARIS, MalikBORZACCHIELLO, DomenicoAGUADO, Jose VicenteCHINESTA, FranciscoThis paper is concerned with the solution to structural dynamics equations. The technique here presented is closely related to Harmonic Analysis, and therefore it is only concerned with the long-term forced response. Proper Generalized Decomposition (PGD) is used to compute space-frequency separated representations by considering the frequency as an extra coordinate. This formulation constitutes an alternative to classical methods such as Modal Analysis and it is especially advantageous when parametrized structural dynamics equations are of interest. In such case, there is no need to solve the parametrized eigenvalue problem and the space-time solution can be recovered with a Fourier inverse transform. The PGD solution is valid for any forcing term that can be written as a combination of the considered frequencies. Finally, the solution is available for any value of the parameter. When the problem involves frequency-dependent parameters the proposed technique provides a specially suitable method that becomes computationally more efficient when it is combined with a modal representation.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.