https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Fri, 15 May 2026 04:02:52 GMT 2026-05-15T04:02:52Z http://hdl.handle.net/10985/16697 Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading NASRI, Mohamed Aziz; ROBERT, Camille; AMMAR, Amine; EL AREM, Saber; MOREL, Franck The numerical modelling of the behaviour of materials at the microstructural scale has been greatly developed over the last two decades. Unfortunately, conventional resolution methods cannot simulate polycrystalline aggregates beyond tens of loading cycles, and they do not remain quantitative due to the plasticity behaviour. This work presents the development of a numerical solver for the resolution of the Finite Element modelling of polycrystalline aggregates subjected to cyclic mechanical loading. The method is based on two concepts. The first one consists in maintaining a constant stiffness matrix. The second uses a time/space model reduction method. In order to analyse the applicability and the performance of the use of a space–time separated representation, the simulations are carried out on a three-dimensional polycrystalline aggregate under cyclic loading. Different numbers of elements per grain and two time increments per cycle are investigated. The results show a significant CPU time saving while maintaining good precision. Moreover, increasing the number of elements and the number of time increments per cycle, the model reduction method is faster than the standard solver. Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/10985/16697 2018-01-01T00:00:00Z NASRI, Mohamed Aziz ROBERT, Camille AMMAR, Amine EL AREM, Saber MOREL, Franck The numerical modelling of the behaviour of materials at the microstructural scale has been greatly developed over the last two decades. Unfortunately, conventional resolution methods cannot simulate polycrystalline aggregates beyond tens of loading cycles, and they do not remain quantitative due to the plasticity behaviour. This work presents the development of a numerical solver for the resolution of the Finite Element modelling of polycrystalline aggregates subjected to cyclic mechanical loading. The method is based on two concepts. The first one consists in maintaining a constant stiffness matrix. The second uses a time/space model reduction method. In order to analyse the applicability and the performance of the use of a space–time separated representation, the simulations are carried out on a three-dimensional polycrystalline aggregate under cyclic loading. Different numbers of elements per grain and two time increments per cycle are investigated. The results show a significant CPU time saving while maintaining good precision. Moreover, increasing the number of elements and the number of time increments per cycle, the model reduction method is faster than the standard solver. http://hdl.handle.net/10985/17206 On a systematic approach for cracked rotating shaft study: breathing mechanism, dynamics and instability BEN ZID, Maha; EL AREM, Saber We present a systematic approach to deal with the modeling and analysis of the cracked rotating shafts behaviour. We begin by revisiting the problem of modelling the breathing mechanism of the crack. Here we consider an original approach based on the form we give to the energy of the system and then identify the mechanism parameters using 3D computations with unilateral contact conditions on the crack lips. A dimensionless flexibility is identified which makes the application of the approach to similar problems straightforward. The additional flexibility due to the crack is then introduced in a simple and comprehensive dynamical system (2 DOF) to characterize the crack effects on the dynamical response of a rotating shaft. Many results could help in early crack detection. The EDF LMS model for the mechanics of cracked rotating shaft Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/10985/17206 2017-01-01T00:00:00Z BEN ZID, Maha EL AREM, Saber We present a systematic approach to deal with the modeling and analysis of the cracked rotating shafts behaviour. We begin by revisiting the problem of modelling the breathing mechanism of the crack. Here we consider an original approach based on the form we give to the energy of the system and then identify the mechanism parameters using 3D computations with unilateral contact conditions on the crack lips. A dimensionless flexibility is identified which makes the application of the approach to similar problems straightforward. The additional flexibility due to the crack is then introduced in a simple and comprehensive dynamical system (2 DOF) to characterize the crack effects on the dynamical response of a rotating shaft. Many results could help in early crack detection. http://hdl.handle.net/10985/17204 Nonlinear analysis, instability and routes to chaos of a cracked rotating shaft EL AREM, Saber The aim of this paper is to explore the dynamical response of a rotating shaft with a cracked transverse section. This complex problem is distilled down to the study of a very comprehensive mechanical system composed of two non-cracked rigid bars connected with a nonlinear bending spring that concentrates the global stiffness of the cracked shaft. The switching crack model is presented as a specific case of the EDF-LMS family of models and adopted to describe the breathing mechanism of the crack. By analyzing the system equilibrium equations, we show that the stiffness change when the crack breathes leads to shocks with velocity jumps and coupling between the transverse oscillations. The linear stability of the periodic solutions is examined based on the Floquet’s theory. Nonlinear dynamics tools such as Poincaré maps and bifurcation diagrams are used to unveil the system oscillations characteristics. Many well-known features due to the crack presence have been observed, but some unexpected responses are noticed like chaotic behavior. This can be confidently attributed to the abrupt change of the structure stiffness with the breathing crack. It has also been observed that with the super-harmonic resonance phenomenon, the increase of static deflection accompanied by that of the first two harmonics amplitudes are good indicators of a propagating crack presence. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/17204 2019-01-01T00:00:00Z EL AREM, Saber The aim of this paper is to explore the dynamical response of a rotating shaft with a cracked transverse section. This complex problem is distilled down to the study of a very comprehensive mechanical system composed of two non-cracked rigid bars connected with a nonlinear bending spring that concentrates the global stiffness of the cracked shaft. The switching crack model is presented as a specific case of the EDF-LMS family of models and adopted to describe the breathing mechanism of the crack. By analyzing the system equilibrium equations, we show that the stiffness change when the crack breathes leads to shocks with velocity jumps and coupling between the transverse oscillations. The linear stability of the periodic solutions is examined based on the Floquet’s theory. Nonlinear dynamics tools such as Poincaré maps and bifurcation diagrams are used to unveil the system oscillations characteristics. Many well-known features due to the crack presence have been observed, but some unexpected responses are noticed like chaotic behavior. This can be confidently attributed to the abrupt change of the structure stiffness with the breathing crack. It has also been observed that with the super-harmonic resonance phenomenon, the increase of static deflection accompanied by that of the first two harmonics amplitudes are good indicators of a propagating crack presence. http://hdl.handle.net/10985/23141 Rupture Nucleation on a Periodically Heterogeneous Interface GOUNON, Alisson; LATOUR, Soumaya; LETORT, Jean; EL AREM, Saber Abstract In this study we explore experimentally the effects of fault heterogeneity on the rupture nucleation. We conducted friction experiments between two polycarbonate plates, with a periodically heterogeneous friction interface. The rupture propagation is monitored with an ultra-fast video camera by taking advantage of the photo-elastic properties of the material used. We show that the nucleation process does not always consists of a monotonic growth of the rupture velocity. Instead, the rupture front advances with an alternation of slow and fast episodes that accelerates until it reaches a point at which fast propagation dominates. This complex nucleation process is compared to the results predicted by previous numerical studies on heterogeneous interfaces. Finally, we test whether it is possible to describe this complex nucleation process as a homogenized nucleation. We also point out a large variability in the rupture process due to the uncontrolled stress heterogeneity that occurs during the loading process. Thu, 06 Oct 2022 00:00:00 GMT http://hdl.handle.net/10985/23141 2022-10-06T00:00:00Z GOUNON, Alisson LATOUR, Soumaya LETORT, Jean EL AREM, Saber Abstract In this study we explore experimentally the effects of fault heterogeneity on the rupture nucleation. We conducted friction experiments between two polycarbonate plates, with a periodically heterogeneous friction interface. The rupture propagation is monitored with an ultra-fast video camera by taking advantage of the photo-elastic properties of the material used. We show that the nucleation process does not always consists of a monotonic growth of the rupture velocity. Instead, the rupture front advances with an alternation of slow and fast episodes that accelerates until it reaches a point at which fast propagation dominates. This complex nucleation process is compared to the results predicted by previous numerical studies on heterogeneous interfaces. Finally, we test whether it is possible to describe this complex nucleation process as a homogenized nucleation. We also point out a large variability in the rupture process due to the uncontrolled stress heterogeneity that occurs during the loading process. http://hdl.handle.net/10985/19267 On cracked rotating shaft mechanics: a systematic approach BEN ZID, Maha; EL AREM, Saber We present a systematic approach to deal with the modeling and analysis of the cracked rotating shafts behaviour. We begin by revisiting the problem of modelling the breathing mechanism ofthe crack. Here we consider an original approach based on the form we give to the energy of the system and then identify the mechanism parameters using 3D computations with unilateral contact conditions on the crack lips. A dimensionless flexibility is identified which makes the application of the approach to similar problems straightforward. The additional flexibility due to the crack is then introduced in a simple and comprehensive dynamical system (2 DOF) to characterize the crack effects on the dynamical response of a rotating shaft. Many results could help in early crack detection. Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/10985/19267 2017-01-01T00:00:00Z BEN ZID, Maha EL AREM, Saber We present a systematic approach to deal with the modeling and analysis of the cracked rotating shafts behaviour. We begin by revisiting the problem of modelling the breathing mechanism ofthe crack. Here we consider an original approach based on the form we give to the energy of the system and then identify the mechanism parameters using 3D computations with unilateral contact conditions on the crack lips. A dimensionless flexibility is identified which makes the application of the approach to similar problems straightforward. The additional flexibility due to the crack is then introduced in a simple and comprehensive dynamical system (2 DOF) to characterize the crack effects on the dynamical response of a rotating shaft. Many results could help in early crack detection. http://hdl.handle.net/10985/19260 A phase‐field model for brittle fracture of anisotropic materials GMATI, Hela; MAREAU, Charles; AMMAR, Amine; EL AREM, Saber In the present work, a phase field damage model is developed to address the numerical simulation of brittle fracture. This model successfully captures some important aspects of crack propagation, including crack branching and bifurcation. In addition, the proposed phase field model has been developed in the general framework of anisotropic elasticity. It can thus be used for the simulation of brittle fracture in polycrystalline materials, for which crack propagation is impacted by crystallographic orientation because of the anisotropic character of stiffness properties. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/19260 2020-01-01T00:00:00Z GMATI, Hela MAREAU, Charles AMMAR, Amine EL AREM, Saber In the present work, a phase field damage model is developed to address the numerical simulation of brittle fracture. This model successfully captures some important aspects of crack propagation, including crack branching and bifurcation. In addition, the proposed phase field model has been developed in the general framework of anisotropic elasticity. It can thus be used for the simulation of brittle fracture in polycrystalline materials, for which crack propagation is impacted by crystallographic orientation because of the anisotropic character of stiffness properties. http://hdl.handle.net/10985/19261 On the mechanics of beams and shafts with cracks: A standard and generic approach EL AREM, Saber A generic methodology to deal with the mechanics of beams and shafts with cracks is presented. The elastic energy of the system under static loading is written in a comprehensive manner to remarkably reduce the 3D computations indispensable to the identification of the crack breathing mechanism. With a new reformulation of the problem, the breathing mechanism identification is distilled down to the computation of a dimensionless function that gives a fine and precise description of the system flexibility evolution when the crack breathes. This breathing function is exclusively inherent to the crack geometry and completely independent of the 3D model parameters which makes the approach more universal and could be applied straightforward to similar problems. This standard and generic methodology is completed by a detailed description of the technique of construction of a Cracked Beam Finite Element. Moreover, we give a nonlinear fitting formula of the identified function that all the process of identification could be skipped when a cracked transverse section is to be inserted in a beam-like model of a cracked shaft. A validation of the approach under static loading is given for a cantilever beam with one, then two cracked transverse sections. We also show, for a simple cracked shaft, common features of its vibrational behavior. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/19261 2020-01-01T00:00:00Z EL AREM, Saber A generic methodology to deal with the mechanics of beams and shafts with cracks is presented. The elastic energy of the system under static loading is written in a comprehensive manner to remarkably reduce the 3D computations indispensable to the identification of the crack breathing mechanism. With a new reformulation of the problem, the breathing mechanism identification is distilled down to the computation of a dimensionless function that gives a fine and precise description of the system flexibility evolution when the crack breathes. This breathing function is exclusively inherent to the crack geometry and completely independent of the 3D model parameters which makes the approach more universal and could be applied straightforward to similar problems. This standard and generic methodology is completed by a detailed description of the technique of construction of a Cracked Beam Finite Element. Moreover, we give a nonlinear fitting formula of the identified function that all the process of identification could be skipped when a cracked transverse section is to be inserted in a beam-like model of a cracked shaft. A validation of the approach under static loading is given for a cantilever beam with one, then two cracked transverse sections. We also show, for a simple cracked shaft, common features of its vibrational behavior. 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; EL AREM, Saber; MOREL, Franck; 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 GMT http://hdl.handle.net/10985/10755 2015-01-01T00:00:00Z NASRI, Mohamed Aziz ROBERT, Camille EL AREM, Saber MOREL, Franck 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 http://hdl.handle.net/10985/10754 On the Model Order Reduction of Confined Plasticity NASRI, Mohamed Aziz; AMMAR, Amine; CHINESTA SORIA, Francisco; ROBERT, Camille; EL AREM, Saber; MOREL, Franck 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. In some processes, plastic deformations remain very localized, for example in the immediate neighborhood of the surface. In that case, the in-plane characteristic dimension is several orders of magnitude higher than the one related to the deepness in which plasticity localizes. In those situations the use of standard mesh-based 3D discretization is challenging because the extremely different characteristic dimensions that to capture all the information requires the use of millions of nodes. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/10985/10754 2016-01-01T00:00:00Z NASRI, Mohamed Aziz AMMAR, Amine CHINESTA SORIA, Francisco ROBERT, Camille EL AREM, Saber MOREL, Franck 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. In some processes, plastic deformations remain very localized, for example in the immediate neighborhood of the surface. In that case, the in-plane characteristic dimension is several orders of magnitude higher than the one related to the deepness in which plasticity localizes. In those situations the use of standard mesh-based 3D discretization is challenging because the extremely different characteristic dimensions that to capture all the information requires the use of millions of nodes. 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 GMT http://hdl.handle.net/10985/10760 2015-01-01T00:00:00Z NASRI, Mohamed Aziz ROBERT, Camille MOREL, Franck EL AREM, Saber AMMAR, Amine none