Nadia FAKRI - Academia.edu (original) (raw)

Papers by Nadia FAKRI

Research paper thumbnail of Nonlinear micromechanical modeling of fully coupled piezo-elastic composite under large deformation and high electric field

Research paper thumbnail of Modeling of Thermo-Electro-Elastic Effective Behaviors of Piezoelectric Composite Mediums and Analysis of Reinforcement Orientation Effects

Solid Mechanics and Its Applications, 2004

In this paper a thermo-electro-elastic modeling for piezoelectric inclusions in an infinite non-p... more In this paper a thermo-electro-elastic modeling for piezoelectric inclusions in an infinite non-piezoelectric matrix is proposed. Extension of the heterogeneous inclusion problem of Eshelby for elastic to electroelastic behavior is formulated in terms of four interaction tensors. These tensors are basically used to derive the self-consistent model and Mori-Tanaka approaches for ellipsoidal piezoelectric inclusions. Solutions are based on numerical computations of these tensors for various types of inclusions. Using the obtained results, effective thermo-electro-elastic moduli of piezoelectric multiphase composites are investigated by an iterative procedure in the context of self-consistent scheme. The influence of the pooling direction effect on the thermo-electro-elastic coefficients is studied and several numerical tests of Ceramic/Epoxy composites are investigated.

Research paper thumbnail of Texture Transition, Micro Shear Bands and Heterogeneous Plastic Strain in F.C.C. and B.C.C. Metals in Rolling

Textures and Microstructures, 1988

Research paper thumbnail of Thermal and Electroelastic Behavior of Piezocomposites and Inhomogeneous Piezoelectric Materials with Voids

Journal of Intelligent Material Systems and Structures, 2009

This article presents an incremental self-consistent model that is used to optimize two kinds of ... more This article presents an incremental self-consistent model that is used to optimize two kinds of thermoelectroelastic composites: polymer/ceramic and ceramic/void. The modeling is based on the heterogeneous inclusion problem of Eshelby, which leads to an expression for the strain−electric field relation by integral equations. The solution of these equations leads to expressions for electroelastic concentration tensors based on a micromechanical model. The overall thermal and electroelastic behavior of the composites considered can be estimated by means of these concentration tensors. An incremental self-consistent scheme is introduced that improves upon the classical self-consistent model for piezoelectric composites. Predictions using this scheme are compared to predictions based on the Mori−Tanaka and self-consistent models of the thermal and electroelastic behavior of inhomogeneous piezoelectric materials with and without void inclusions. The effects of poling direction and inclu...

Research paper thumbnail of Electroelastic behavior modeling of piezoelectric composite materials containing spatially oriented reinforcements

International Journal of Solids and Structures, 2003

ABSTRACT In this work, a modeling of electroelastic composite materials is proposed. The extensio... more ABSTRACT In this work, a modeling of electroelastic composite materials is proposed. The extension of the heterogeneous inclusion problem of Eshelby for elastic to electroelastic behavior is formulated in terms of four interaction tensors related to Eshelby’s electroelastic tensors. Analytical formulations of interaction tensors are presented for ellipsoidal inclusions. These tensors are basically used to derive the self-consistent model, Mori–Tanaka and dilute approaches. Numerical solutions are based on numerical computations of these tensors for various types of inclusions. Using the obtained results, effective electroelastic moduli of piezoelectric multiphase composites are investigated by an iterative procedure in the context of self-consistent scheme. Generalised Mori–Tanaka’s model and dilute approach are re-formulated and the three models are deeply analysed. Concentration tensors corresponding to each model are presented and relationships of effective coefficients are given. Numerical results of effective electroelastic moduli are presented for various types of piezoelectric inclusions and for various orientations and compared to existing experimental and theoretical ones.

Research paper thumbnail of The role of shear bands in the evolution of copper texture

International Journal of Plasticity, 1992

This work brings the results of the modeling of the effect of shear banding upon the evolution of... more This work brings the results of the modeling of the effect of shear banding upon the evolution of the texture in copper. The starting points for this study are the experimental observations which show that small secondary deformation, imposed along a new strain path, causes a significant change of the metal texture under the conditions of highly localized deformation (shear banding). Calculations of the texture evolution were performed for three variants of the model which differ in the aspect (homo or heterogeneous) and the mode (multislip or transgranular shear) of deformation during secondary straining. The best fit of the experimental and calculated textures was obtained when the secondary deformation was considered as highly localized, transgranular shear in a "single system" and lattice rotations caused by two families of symmetrical (but not evenly distributed) bands that were superposed.

Research paper thumbnail of Flutter and parametric stability analysis of axially moving composite graphene sheets

MATEC Web of Conferences, 2019

The dynamic analysis instability of axially moving rectangular composite graphene sheets with vis... more The dynamic analysis instability of axially moving rectangular composite graphene sheets with visco elastic foundation is modeled and numerically simulated for various boundary conditions based on the differential quadrature method (DQM). The partial differential equation of motion based on the nonlocal elasticity and the Kirchhoff plate theories is given. The Galerkin and harmonic balance methods are used for the linear and parametric vibration analysis. The influences of nonlocal parameter, the fibers orientation and the viscoelastic foundation effects on the dynamic behaviors of the rectangular graphene sheet as well as the instabilities induced by the time dependent axial speed and its excitation frequency are investigated.

Research paper thumbnail of Modélisation micromécanique du comportement thermique et électro - élastique effectif de matériaux composites piézoélectriques

Research paper thumbnail of Mathematical modeling of fully coupled reinforced Magneto-Electro-Thermo-Mechanical effective properties based on conditioned micromechanics

Composite Structures, 2021

Research paper thumbnail of Hétérogénéités de déformation plastique induites et conséquences sur la formation des bandes de cisaillement et des textures de déformation

La deformation plastique des polycristaux metalliques presente generalement des heterogeneites a ... more La deformation plastique des polycristaux metalliques presente generalement des heterogeneites a la fois a l'echelle granulaire et du polycristal. Ces heterogeneites peuvent se manifester sous forme de microbandes de cisaillement dans les grains du polycristal ou de bandes macroscopiques traversant plusieurs grains dans une orientation bien determinee. La modelisation de ce phenomene, aussi bien a l'echelle du grain qu'a celle du polycristal, montre le role tres important que jouent ces heterogeneites plastiques dans l'evolution de la texture de deformation

Research paper thumbnail of Well conditioned mathematical modeling for homogenization of thermo-electro-mechanical behaviors of piezoelectric composites

Applied Mathematical Modelling, 2021

Abstract In the present paper, a mathematical modeling of effective properties of fully coupled t... more Abstract In the present paper, a mathematical modeling of effective properties of fully coupled thermo-electro-mechanical heterogeneous materials is elaborated. Constitutive equations combined with equilibrium equations lead to a coupled partial differential system. A methodological procedure is elaborated based on thermo-electro-elastic Green’s functions, integral equations, and a micro-macro approach. Localization tensors are derived using the Mori–Tanaka mean-field assumptions and the fully coupled effective behavior is obtained through averaging techniques. Due to the large dispersion between elastic, dielectric, and piezoelectric coefficients ill-conditioned localization tensors are resulted. Block matrix decomposition is elaborated to overcome this drawback and the so-regularized localization tensor’s inverses are used to get a well conditioned problem. Numerical computations are done in the general case of ellipsoidal inclusions and anisotropic behavior. Effective thermal conductivity and heat capacity coefficients are obtained with and without the heat strain effect for various volume fractions and types of inclusions. The global properties of thermo-electro-elastic reinforced composites are presented with respect to shape and volume fractions of inclusions.

Research paper thumbnail of Regularized Micromechanical Modeling for the Prediction of Electro-Elastic Behavior of Reinforced Piezoelectric Composites

2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), 2021

Research paper thumbnail of Nonlinear micromechanical modeling of fully coupled piezo-elastic composite under large deformation and high electric field

Research paper thumbnail of Modeling of Thermo-Electro-Elastic Effective Behaviors of Piezoelectric Composite Mediums and Analysis of Reinforcement Orientation Effects

Solid Mechanics and Its Applications, 2004

In this paper a thermo-electro-elastic modeling for piezoelectric inclusions in an infinite non-p... more In this paper a thermo-electro-elastic modeling for piezoelectric inclusions in an infinite non-piezoelectric matrix is proposed. Extension of the heterogeneous inclusion problem of Eshelby for elastic to electroelastic behavior is formulated in terms of four interaction tensors. These tensors are basically used to derive the self-consistent model and Mori-Tanaka approaches for ellipsoidal piezoelectric inclusions. Solutions are based on numerical computations of these tensors for various types of inclusions. Using the obtained results, effective thermo-electro-elastic moduli of piezoelectric multiphase composites are investigated by an iterative procedure in the context of self-consistent scheme. The influence of the pooling direction effect on the thermo-electro-elastic coefficients is studied and several numerical tests of Ceramic/Epoxy composites are investigated.

Research paper thumbnail of Texture Transition, Micro Shear Bands and Heterogeneous Plastic Strain in F.C.C. and B.C.C. Metals in Rolling

Textures and Microstructures, 1988

Research paper thumbnail of Thermal and Electroelastic Behavior of Piezocomposites and Inhomogeneous Piezoelectric Materials with Voids

Journal of Intelligent Material Systems and Structures, 2009

This article presents an incremental self-consistent model that is used to optimize two kinds of ... more This article presents an incremental self-consistent model that is used to optimize two kinds of thermoelectroelastic composites: polymer/ceramic and ceramic/void. The modeling is based on the heterogeneous inclusion problem of Eshelby, which leads to an expression for the strain−electric field relation by integral equations. The solution of these equations leads to expressions for electroelastic concentration tensors based on a micromechanical model. The overall thermal and electroelastic behavior of the composites considered can be estimated by means of these concentration tensors. An incremental self-consistent scheme is introduced that improves upon the classical self-consistent model for piezoelectric composites. Predictions using this scheme are compared to predictions based on the Mori−Tanaka and self-consistent models of the thermal and electroelastic behavior of inhomogeneous piezoelectric materials with and without void inclusions. The effects of poling direction and inclu...

Research paper thumbnail of Electroelastic behavior modeling of piezoelectric composite materials containing spatially oriented reinforcements

International Journal of Solids and Structures, 2003

ABSTRACT In this work, a modeling of electroelastic composite materials is proposed. The extensio... more ABSTRACT In this work, a modeling of electroelastic composite materials is proposed. The extension of the heterogeneous inclusion problem of Eshelby for elastic to electroelastic behavior is formulated in terms of four interaction tensors related to Eshelby’s electroelastic tensors. Analytical formulations of interaction tensors are presented for ellipsoidal inclusions. These tensors are basically used to derive the self-consistent model, Mori–Tanaka and dilute approaches. Numerical solutions are based on numerical computations of these tensors for various types of inclusions. Using the obtained results, effective electroelastic moduli of piezoelectric multiphase composites are investigated by an iterative procedure in the context of self-consistent scheme. Generalised Mori–Tanaka’s model and dilute approach are re-formulated and the three models are deeply analysed. Concentration tensors corresponding to each model are presented and relationships of effective coefficients are given. Numerical results of effective electroelastic moduli are presented for various types of piezoelectric inclusions and for various orientations and compared to existing experimental and theoretical ones.

Research paper thumbnail of The role of shear bands in the evolution of copper texture

International Journal of Plasticity, 1992

This work brings the results of the modeling of the effect of shear banding upon the evolution of... more This work brings the results of the modeling of the effect of shear banding upon the evolution of the texture in copper. The starting points for this study are the experimental observations which show that small secondary deformation, imposed along a new strain path, causes a significant change of the metal texture under the conditions of highly localized deformation (shear banding). Calculations of the texture evolution were performed for three variants of the model which differ in the aspect (homo or heterogeneous) and the mode (multislip or transgranular shear) of deformation during secondary straining. The best fit of the experimental and calculated textures was obtained when the secondary deformation was considered as highly localized, transgranular shear in a "single system" and lattice rotations caused by two families of symmetrical (but not evenly distributed) bands that were superposed.

Research paper thumbnail of Flutter and parametric stability analysis of axially moving composite graphene sheets

MATEC Web of Conferences, 2019

The dynamic analysis instability of axially moving rectangular composite graphene sheets with vis... more The dynamic analysis instability of axially moving rectangular composite graphene sheets with visco elastic foundation is modeled and numerically simulated for various boundary conditions based on the differential quadrature method (DQM). The partial differential equation of motion based on the nonlocal elasticity and the Kirchhoff plate theories is given. The Galerkin and harmonic balance methods are used for the linear and parametric vibration analysis. The influences of nonlocal parameter, the fibers orientation and the viscoelastic foundation effects on the dynamic behaviors of the rectangular graphene sheet as well as the instabilities induced by the time dependent axial speed and its excitation frequency are investigated.

Research paper thumbnail of Modélisation micromécanique du comportement thermique et électro - élastique effectif de matériaux composites piézoélectriques

Research paper thumbnail of Mathematical modeling of fully coupled reinforced Magneto-Electro-Thermo-Mechanical effective properties based on conditioned micromechanics

Composite Structures, 2021

Research paper thumbnail of Hétérogénéités de déformation plastique induites et conséquences sur la formation des bandes de cisaillement et des textures de déformation

La deformation plastique des polycristaux metalliques presente generalement des heterogeneites a ... more La deformation plastique des polycristaux metalliques presente generalement des heterogeneites a la fois a l'echelle granulaire et du polycristal. Ces heterogeneites peuvent se manifester sous forme de microbandes de cisaillement dans les grains du polycristal ou de bandes macroscopiques traversant plusieurs grains dans une orientation bien determinee. La modelisation de ce phenomene, aussi bien a l'echelle du grain qu'a celle du polycristal, montre le role tres important que jouent ces heterogeneites plastiques dans l'evolution de la texture de deformation

Research paper thumbnail of Well conditioned mathematical modeling for homogenization of thermo-electro-mechanical behaviors of piezoelectric composites

Applied Mathematical Modelling, 2021

Abstract In the present paper, a mathematical modeling of effective properties of fully coupled t... more Abstract In the present paper, a mathematical modeling of effective properties of fully coupled thermo-electro-mechanical heterogeneous materials is elaborated. Constitutive equations combined with equilibrium equations lead to a coupled partial differential system. A methodological procedure is elaborated based on thermo-electro-elastic Green’s functions, integral equations, and a micro-macro approach. Localization tensors are derived using the Mori–Tanaka mean-field assumptions and the fully coupled effective behavior is obtained through averaging techniques. Due to the large dispersion between elastic, dielectric, and piezoelectric coefficients ill-conditioned localization tensors are resulted. Block matrix decomposition is elaborated to overcome this drawback and the so-regularized localization tensor’s inverses are used to get a well conditioned problem. Numerical computations are done in the general case of ellipsoidal inclusions and anisotropic behavior. Effective thermal conductivity and heat capacity coefficients are obtained with and without the heat strain effect for various volume fractions and types of inclusions. The global properties of thermo-electro-elastic reinforced composites are presented with respect to shape and volume fractions of inclusions.

Research paper thumbnail of Regularized Micromechanical Modeling for the Prediction of Electro-Elastic Behavior of Reinforced Piezoelectric Composites

2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), 2021