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Papers by khalil Mansouri
Le Centre pour la Communication Scientifique Directe - HAL - UJM - Université Jean Monnet, May 16, 2022
Nous proposons une procédure pour approcher le comportement des nappes composites à matrice caout... more Nous proposons une procédure pour approcher le comportement des nappes composites à matrice caoutchouteuse par une méthode d'homogénéisation à deux échelles. Cette méthode est dérivée de celle proposée par Terada et al.[1] qui consiste en un découplage des échelles micro et macro en considérant des problèmes aux limites (PL) séparés. Les PL micro-et macroscopiques non linéaires à deux échelles sont fortement couplés dans la plupart des méthodes d'homogénéisation. La méthode considérée nous permet de les découpler sans perdre les caractéristiques distinctes du PL à deux échelles. En d'autres termes, avec cette méthode, la solution du problème macroscopique reflète le comportement mécanique du problème microscopique, et vice versa. Nous effectuons des études numériques représentatives pour une nappe avec un matériau hétérogène hyperélastique afin de démontrer la capacité et la fiabilité de la méthode proposée. Mots clés-hyperélasticité, méthode d'homogénéisation, découplage.
This study is a numerical analysis of the industrial quenching process for leaf springs developed... more This study is a numerical analysis of the industrial quenching process for leaf springs developed by the CAVEO company. The leaf chosen for this study is of a parabolic profile made of EN-51CrV4 steel (AISI 6150). The aim of this study is to set up a numerical model to predict thermal, metallurgical, and mechanical behavior of a leaf spring from exit of the heating furnace to exit of the quenching bath going through a cambering operation. This study would therefore allow the company to switch from a development scheme based on experiments using physical prototypes tested on the production line to a new scheme based on virtual prototypes using numerical simulation. The development of the numerical model using the finite element method is carried out using the ABAQUS/Implicit solver coupled with two user subroutines Phase and UMAT. The first one have been developed to compute microstructure evolution and the second one to define the constitutive law taking into account phase transform...
International Journal of Engineering Science, 2018
The boundary-value problem of Neo-Hookean incompressible hyperelastic cracked solid under a super... more The boundary-value problem of Neo-Hookean incompressible hyperelastic cracked solid under a superposition of a plane deformation to an anti-plane one is formulated. An asymptotic analysis is then employed to compute the elastostatic fields near the crack front and their principal properties are illustrated. In a particular basis, the crack is bound to open independently of the magnitude and the mode of the boundary conditions at infinity. The stress field components have different singularities and each one can posses more than one singular term. Some disagreements with the linear theory are evidenced.
International Journal for Numerical Methods in Engineering, 2014
The present work aims to look into the contribution of the extended nite element method for large... more The present work aims to look into the contribution of the extended nite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sucient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, since it serves as an Xfem enrichment basis. nally, a convergence study is carried out to show the contribution of the exploitation of such method.
European Journal of Computational Mechanics, 2012
un problème d'élasticité incompressible dans un domaine fissuré. L'objectif est d'étendre l'étude... more un problème d'élasticité incompressible dans un domaine fissuré. L'objectif est d'étendre l'étude faite sur la variante X-FEM cutoff , dans le cas de l'élasticité compressible, au comportement incompressible. Une preuve mathématique de la condition inf-sup de la formulation mixte discrète avec X-FEM est établie pour certains champs enrichis. Nous donnons également un résultat mathématique de la quasi-optimalité de l'estimation d'erreur. Enfin, nous validons ces résultats avec des tests numériques.
Comptes Rendus Mécanique, 2008
This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under ... more This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under general far-field loading conditions. The analysis is based on the finite plane deformation hyperelasticity theory for an incompressible Mooney-Rivlin material. We approach the solution, near the singularity, by a mixed asymptotic development. We show that the shape of the solution depends on the opening angle of the notch and that there is singularity if the notch is concave. Furthermore, we show that a pure loading mode II gives rise to the opening of the notch vertex in contrast to the linear elasticity. To cite this article: M.
International Journal of Solids and Structures, 2015
Comptes Rendus Mécanique, 2008
This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under ... more This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under general far-field loading conditions. The analysis is based on the finite plane deformation hyperelasticity theory for an incompressible Mooney-Rivlin material. We approach the solution, near the singularity, by a mixed asymptotic development. We show that the shape of the solution depends on the opening angle of the notch and that there is singularity if the notch is concave. Furthermore, we show that a pure loading mode II gives rise to the opening of the notch vertex in contrast to the linear elasticity. To cite this article: M. Arfaoui et al., C. R. Mecanique 336 (2008).
International Journal for Numerical Methods in Engineering
The present work aims to look into the contribution of the extended finite element method for lar... more The present work aims to look into the contribution of the extended finite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sufficient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, because it serves as an eXtended finite element method enrichment basis. Finally, a convergence study is carried out to show the contribution of the exploitation of such method. Copyright © 2014 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
The present work aims to look into the contribution of the extended finite element method for lar... more The present work aims to look into the contribution of the extended finite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sufficient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, because it serves as an eXtended finite element method enrichment basis. Finally, a convergence study is carried out to show the contribution of the exploitation of such method. Copyright © 2014 John Wiley & Sons, Ltd.
The aim of this paper is to study numerical convergence and stability of mixed formulation of X-F... more The aim of this paper is to study numerical convergence and stability of mixed formulation of X-FEM cut-off for incompressible isotropic linear plane elasticity problem in a cracked domain using a cut-off function to localize the singular enrichment area. The difficulty is caused by both, the so called infsup condition which depends on the connection between the approximation spaces for the displacement and pressure, and the discontinuity of the displacement field across the crack. We prove that a quasioptimal convergence rate holds in spite of the presence of elements cut by the crack.
Le Centre pour la Communication Scientifique Directe - HAL - UJM - Université Jean Monnet, May 16, 2022
Nous proposons une procédure pour approcher le comportement des nappes composites à matrice caout... more Nous proposons une procédure pour approcher le comportement des nappes composites à matrice caoutchouteuse par une méthode d'homogénéisation à deux échelles. Cette méthode est dérivée de celle proposée par Terada et al.[1] qui consiste en un découplage des échelles micro et macro en considérant des problèmes aux limites (PL) séparés. Les PL micro-et macroscopiques non linéaires à deux échelles sont fortement couplés dans la plupart des méthodes d'homogénéisation. La méthode considérée nous permet de les découpler sans perdre les caractéristiques distinctes du PL à deux échelles. En d'autres termes, avec cette méthode, la solution du problème macroscopique reflète le comportement mécanique du problème microscopique, et vice versa. Nous effectuons des études numériques représentatives pour une nappe avec un matériau hétérogène hyperélastique afin de démontrer la capacité et la fiabilité de la méthode proposée. Mots clés-hyperélasticité, méthode d'homogénéisation, découplage.
This study is a numerical analysis of the industrial quenching process for leaf springs developed... more This study is a numerical analysis of the industrial quenching process for leaf springs developed by the CAVEO company. The leaf chosen for this study is of a parabolic profile made of EN-51CrV4 steel (AISI 6150). The aim of this study is to set up a numerical model to predict thermal, metallurgical, and mechanical behavior of a leaf spring from exit of the heating furnace to exit of the quenching bath going through a cambering operation. This study would therefore allow the company to switch from a development scheme based on experiments using physical prototypes tested on the production line to a new scheme based on virtual prototypes using numerical simulation. The development of the numerical model using the finite element method is carried out using the ABAQUS/Implicit solver coupled with two user subroutines Phase and UMAT. The first one have been developed to compute microstructure evolution and the second one to define the constitutive law taking into account phase transform...
International Journal of Engineering Science, 2018
The boundary-value problem of Neo-Hookean incompressible hyperelastic cracked solid under a super... more The boundary-value problem of Neo-Hookean incompressible hyperelastic cracked solid under a superposition of a plane deformation to an anti-plane one is formulated. An asymptotic analysis is then employed to compute the elastostatic fields near the crack front and their principal properties are illustrated. In a particular basis, the crack is bound to open independently of the magnitude and the mode of the boundary conditions at infinity. The stress field components have different singularities and each one can posses more than one singular term. Some disagreements with the linear theory are evidenced.
International Journal for Numerical Methods in Engineering, 2014
The present work aims to look into the contribution of the extended nite element method for large... more The present work aims to look into the contribution of the extended nite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sucient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, since it serves as an Xfem enrichment basis. nally, a convergence study is carried out to show the contribution of the exploitation of such method.
European Journal of Computational Mechanics, 2012
un problème d'élasticité incompressible dans un domaine fissuré. L'objectif est d'étendre l'étude... more un problème d'élasticité incompressible dans un domaine fissuré. L'objectif est d'étendre l'étude faite sur la variante X-FEM cutoff , dans le cas de l'élasticité compressible, au comportement incompressible. Une preuve mathématique de la condition inf-sup de la formulation mixte discrète avec X-FEM est établie pour certains champs enrichis. Nous donnons également un résultat mathématique de la quasi-optimalité de l'estimation d'erreur. Enfin, nous validons ces résultats avec des tests numériques.
Comptes Rendus Mécanique, 2008
This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under ... more This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under general far-field loading conditions. The analysis is based on the finite plane deformation hyperelasticity theory for an incompressible Mooney-Rivlin material. We approach the solution, near the singularity, by a mixed asymptotic development. We show that the shape of the solution depends on the opening angle of the notch and that there is singularity if the notch is concave. Furthermore, we show that a pure loading mode II gives rise to the opening of the notch vertex in contrast to the linear elasticity. To cite this article: M.
International Journal of Solids and Structures, 2015
Comptes Rendus Mécanique, 2008
This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under ... more This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under general far-field loading conditions. The analysis is based on the finite plane deformation hyperelasticity theory for an incompressible Mooney-Rivlin material. We approach the solution, near the singularity, by a mixed asymptotic development. We show that the shape of the solution depends on the opening angle of the notch and that there is singularity if the notch is concave. Furthermore, we show that a pure loading mode II gives rise to the opening of the notch vertex in contrast to the linear elasticity. To cite this article: M. Arfaoui et al., C. R. Mecanique 336 (2008).
International Journal for Numerical Methods in Engineering
The present work aims to look into the contribution of the extended finite element method for lar... more The present work aims to look into the contribution of the extended finite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sufficient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, because it serves as an eXtended finite element method enrichment basis. Finally, a convergence study is carried out to show the contribution of the exploitation of such method. Copyright © 2014 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
The present work aims to look into the contribution of the extended finite element method for lar... more The present work aims to look into the contribution of the extended finite element method for large deformation of cracked bodies in plane strain approximation. The unavailability of sufficient mathematical tools and proofs for such problem makes the study exploratory. First, the asymptotic solution is presented. Then, a numerical analysis is realized to verify the pertinence of solution given by the asymptotic procedure, because it serves as an eXtended finite element method enrichment basis. Finally, a convergence study is carried out to show the contribution of the exploitation of such method. Copyright © 2014 John Wiley & Sons, Ltd.
The aim of this paper is to study numerical convergence and stability of mixed formulation of X-F... more The aim of this paper is to study numerical convergence and stability of mixed formulation of X-FEM cut-off for incompressible isotropic linear plane elasticity problem in a cracked domain using a cut-off function to localize the singular enrichment area. The difficulty is caused by both, the so called infsup condition which depends on the connection between the approximation spaces for the displacement and pressure, and the discontinuity of the displacement field across the crack. We prove that a quasioptimal convergence rate holds in spite of the presence of elements cut by the crack.