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http://hdl.handle.net/10985/14857
On the solution of the heat equation in very thin tapes
PRULIERE, Etienne; CHINESTA, Francisco; AMMAR, Amine; LEYGUE, Adrien; POITOU, Arnaud
This paper addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, / The first issue concerns the necessity of solving the transient model a huge number of times because the thermal loads are moving very fast on the surface of the part and the thermal model is usually non-linear. The second issue concerns the degenerate geometry that we consider in which the thickness is usually much lower than the in-plane characteristic length. The solution of such 3D models involving fine meshes in all the directions becomes rapidly intractable despite the huge recent progresses in computer sciences. In this paper we propose to consider a fully space-time separated representation of the unknown field. This choice allows circumventing both issues allowing the solution of extremely fine models very fast, sometimes in real time.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/148572012-01-01T00:00:00ZPRULIERE, EtienneCHINESTA, FranciscoAMMAR, AmineLEYGUE, AdrienPOITOU, ArnaudThis paper addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, / The first issue concerns the necessity of solving the transient model a huge number of times because the thermal loads are moving very fast on the surface of the part and the thermal model is usually non-linear. The second issue concerns the degenerate geometry that we consider in which the thickness is usually much lower than the in-plane characteristic length. The solution of such 3D models involving fine meshes in all the directions becomes rapidly intractable despite the huge recent progresses in computer sciences. In this paper we propose to consider a fully space-time separated representation of the unknown field. This choice allows circumventing both issues allowing the solution of extremely fine models very fast, sometimes in real time.A reduced model to simulate the damage in composite laminates under low velocity impact
http://hdl.handle.net/10985/14856
A reduced model to simulate the damage in composite laminates under low velocity impact
METOUI, Sondes; PRULIERE, Etienne; AMMAR, Amine; DAU, Frédéric
This article presents an efficient numerical strategy to simulate the damage in composite laminates under low velocity impact. The proposed method is based on a separated representation of the solution in the context of the Proper Generalized Decomposition (PGD). This representation leads to an important reduction of the number of degrees of freedom. In addition to the PGD, the main ingredients of the model are the following: (a) cohesive zone models (CZM) to represent the delamination and the matrix cracking, (b) a modified nonlinear Hertzian contact law to calculate the impact force, (c) the implicit Newmark integration scheme to compute the evolution of the solution during the impact. The method is applied to simulate an impact on a laminated plate. The results are similar to the solution obtained with a classical finite element simulation. The shape of the delaminated area is found to be coherent with some experimental results from the literature.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/148562018-01-01T00:00:00ZMETOUI, SondesPRULIERE, EtienneAMMAR, AmineDAU, FrédéricThis article presents an efficient numerical strategy to simulate the damage in composite laminates under low velocity impact. The proposed method is based on a separated representation of the solution in the context of the Proper Generalized Decomposition (PGD). This representation leads to an important reduction of the number of degrees of freedom. In addition to the PGD, the main ingredients of the model are the following: (a) cohesive zone models (CZM) to represent the delamination and the matrix cracking, (b) a modified nonlinear Hertzian contact law to calculate the impact force, (c) the implicit Newmark integration scheme to compute the evolution of the solution during the impact. The method is applied to simulate an impact on a laminated plate. The results are similar to the solution obtained with a classical finite element simulation. The shape of the delaminated area is found to be coherent with some experimental results from the literature.Elastic calibration of a discrete domain using a proper generalized decomposition
http://hdl.handle.net/10985/19857
Elastic calibration of a discrete domain using a proper generalized decomposition
GIRARDOT, Jérémie; PRULIERE, Etienne
Current discrete/lattice methods can simulate a continuous mechanical behavior thanks to a network of bonds. The main drawback of these approaches is the need of a calibration process to link the emerging behavior of the structure and the parameters of the local mechanical bond. It is proposed in this work to use a fast and recent reduction model technique to build once and for all an exhaustive data chart and thus to avoid the calibration process. The proper generalized decomposition technique was used to build a parametric analysis in the case of a lattice beam structure. The results were in the range of the current calibration values found in the literature and extend it by giving a global calibration curve. They also allowed to discuss about the influence, in this specific case of lattice-beam structure, of the density of beams in terms of number of discrete elements and connectivity.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/198572021-01-01T00:00:00ZGIRARDOT, JérémiePRULIERE, EtienneCurrent discrete/lattice methods can simulate a continuous mechanical behavior thanks to a network of bonds. The main drawback of these approaches is the need of a calibration process to link the emerging behavior of the structure and the parameters of the local mechanical bond. It is proposed in this work to use a fast and recent reduction model technique to build once and for all an exhaustive data chart and thus to avoid the calibration process. The proper generalized decomposition technique was used to build a parametric analysis in the case of a lattice beam structure. The results were in the range of the current calibration values found in the literature and extend it by giving a global calibration curve. They also allowed to discuss about the influence, in this specific case of lattice-beam structure, of the density of beams in terms of number of discrete elements and connectivity.On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition
http://hdl.handle.net/10985/6274
On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition
PRULIERE, Etienne; CHINESTA, Francisco; AMMAR, Amine
This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in mesh-based discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encoun- tered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schrödinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker–Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, etc. This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/62742010-01-01T00:00:00ZPRULIERE, EtienneCHINESTA, FranciscoAMMAR, AmineThis paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in mesh-based discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encoun- tered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schrödinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker–Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, etc. This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations.3D simulation of laminated shell structures using the Proper Generalized Decomposition
http://hdl.handle.net/10985/8489
3D simulation of laminated shell structures using the Proper Generalized Decomposition
PRULIERE, Etienne
Numerical simulations of composite structures are generally performed using multi-layered shell elements in the context of the finite elements method. This strategy has numerous advantages like a low computation time and the capability to reproduce the comportment of composites in most of cases. The main restriction of this approach is that they require an approximation of the comportment in the thickness. This approximation is generally no more valid near the boundary and loading conditions and when non linear phenomena like delamination occurs in the thickness. This paper explores an alternative to shell computation using the framework of the Proper Generalized Decomposition that is based on a separated representation of the solution. The idea is to solve the full 3D solid problem separating the in-plane and the out-of-plane spaces. Practically, a classical shell mesh is used to describe the in-plane geometry and a simple 1D mesh is used to deal with the out-of-plane space. This allows to represents complex fields in the thickness without the complexity and the computation cost of a solid mesh which is particularly interesting when dealing with composite laminates.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/84892014-01-01T00:00:00ZPRULIERE, EtienneNumerical simulations of composite structures are generally performed using multi-layered shell elements in the context of the finite elements method. This strategy has numerous advantages like a low computation time and the capability to reproduce the comportment of composites in most of cases. The main restriction of this approach is that they require an approximation of the comportment in the thickness. This approximation is generally no more valid near the boundary and loading conditions and when non linear phenomena like delamination occurs in the thickness. This paper explores an alternative to shell computation using the framework of the Proper Generalized Decomposition that is based on a separated representation of the solution. The idea is to solve the full 3D solid problem separating the in-plane and the out-of-plane spaces. Practically, a classical shell mesh is used to describe the in-plane geometry and a simple 1D mesh is used to deal with the out-of-plane space. This allows to represents complex fields in the thickness without the complexity and the computation cost of a solid mesh which is particularly interesting when dealing with composite laminates.A reduced numerical strategy based on PGD for composite shell structures simulations
http://hdl.handle.net/10985/7879
A reduced numerical strategy based on PGD for composite shell structures simulations
PRULIERE, Etienne; METOUI, Sondes
This paper explores an alternative to shell computation. The proposed strategy uses the Proper Generalized Methods based on a separated representation. The idea is to solve the full 3D solid problem separating the in-plane and the out-of-plane spaces. This allows to represents complex fields in the thickness without the complexity and the computational cost of a solid mesh which is particularly interesting when dealing with multi-layer composite.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/78792013-01-01T00:00:00ZPRULIERE, EtienneMETOUI, SondesThis paper explores an alternative to shell computation. The proposed strategy uses the Proper Generalized Methods based on a separated representation. The idea is to solve the full 3D solid problem separating the in-plane and the out-of-plane spaces. This allows to represents complex fields in the thickness without the complexity and the computational cost of a solid mesh which is particularly interesting when dealing with multi-layer composite.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.Empirical Natural Closure Relation for Short Fiber Suspension Models
http://hdl.handle.net/10985/6476
Empirical Natural Closure Relation for Short Fiber Suspension Models
PRULIERE, Etienne; AMMAR, Amine; CHINESTA, Francisco
This work focuses on the resolution of the Fokker-Planck equation that governs the evolution of the fibers orientation distribution. To reduce the computing time, that equation is solved along some flow trajectories in order to extract the significant information of the solution from the application of the Karhunen-Loève decomposition. Now, from this information one could solve the Fokker-Planck equation everywhere in the flow domain or simply adjust a closure relation that becomes optimal for such flow, solving the evolution of some orientation moments which require a less amount of computation. This paper focuses on this last strategy. For this purpose we start introducing the Karhunen-Loève decomposition that is applied later to automatically extract the main solution characteristics for adjusting empirically a natural closure relation.
L'auteur Francisco CHINESTA faisait parti en 2007 du Laboratoire de Mécanique des Systèmes et des Procédés (LMSP). Depuis 2010, le LMSP a fusionné avec deux autres unités de recherche en un seul laboratoire intitulé PIMM (Procédés et Ingénierie en Mécanique et Matériaux).
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10985/64762007-01-01T00:00:00ZPRULIERE, EtienneAMMAR, AmineCHINESTA, FranciscoThis work focuses on the resolution of the Fokker-Planck equation that governs the evolution of the fibers orientation distribution. To reduce the computing time, that equation is solved along some flow trajectories in order to extract the significant information of the solution from the application of the Karhunen-Loève decomposition. Now, from this information one could solve the Fokker-Planck equation everywhere in the flow domain or simply adjust a closure relation that becomes optimal for such flow, solving the evolution of some orientation moments which require a less amount of computation. This paper focuses on this last strategy. For this purpose we start introducing the Karhunen-Loève decomposition that is applied later to automatically extract the main solution characteristics for adjusting empirically a natural closure relation.On the solution of the heat equation in very thin tapes
http://hdl.handle.net/10985/8490
On the solution of the heat equation in very thin tapes
PRULIERE, Etienne; CHINESTA, Francisco; AMMAR, Amine; LEYGUE, Adrien; POITOU, Arnaud
This papers addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, ... The first issue concerns the necessity of solving the transient model a huge number of times because the thermal loads are moving very fast on the surface of the part and the thermal model is usually nonlinear. The second issue concerns the degenerate geometry that we consider in which the thickness is usually much lower than the in-plane characteristic length. The solution of such 3D models involving fine meshes in all the directions becomes rapidly intractable despite the huge recent progresses in computer sciences. In this paper we propose to consider a reduced and fully space-time separated representation of the unknown field. This choice allows circumventing both issues allowing the solution of extremely fine models very fast, sometimes in real time.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84902013-01-01T00:00:00ZPRULIERE, EtienneCHINESTA, FranciscoAMMAR, AmineLEYGUE, AdrienPOITOU, ArnaudThis papers addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, ... The first issue concerns the necessity of solving the transient model a huge number of times because the thermal loads are moving very fast on the surface of the part and the thermal model is usually nonlinear. The second issue concerns the degenerate geometry that we consider in which the thickness is usually much lower than the in-plane characteristic length. The solution of such 3D models involving fine meshes in all the directions becomes rapidly intractable despite the huge recent progresses in computer sciences. In this paper we propose to consider a reduced and fully space-time separated representation of the unknown field. This choice allows circumventing both issues allowing the solution of extremely fine models very fast, sometimes in real time.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.