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Mondher Wali

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Fakhreddine Dammak

Dr. Mohammed Tashkandi

Houman Borouchaki

Mohamed Ali REZGUI

IMAEKHAI LAWRENCE

Isfahan University of Technology

madjid Almansba

Mouloud Mammeri University Algeria

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Papers by Mondher Wali

Numerical Formulation of Anisotropic Elastoplastic Behavior Coupled with Damage Model in Forming Processes

Mathematics

The present paper proposes a mathematical development of the plasticity and damage approaches to ... more The present paper proposes a mathematical development of the plasticity and damage approaches to simulate sheet metal forming processes. It focuses on the numerical prediction of the deformation of the sheet metal during the deep drawing process when a crack appears. Anisotropic plasticity constitutive equations are proposed. A fully implicit integration of the coupling constitutive equations is used and leads to two nonlinear local scalar equations that are solved by Newton’s method. The developed model allows predicting the onset of cracks in sheet metals during cold forming operations. The numerical model is implemented in ABAQUS software using user-defined subroutines, which are VUMAT and UMAT. The accuracy of the anisotropic elastoplastic model fully coupled with ductile damage is evaluated using numerical examples.

Mathematical Model Describing the Hardening and Failure Behaviour of Aluminium Alloys: Application in Metal Shear Cutting Process

Mathematics

Recent research has focused on sheet shear cutting operations. However, little research has been ... more Recent research has focused on sheet shear cutting operations. However, little research has been conducted on bar shear cutting. The main objective of the present investigation is to study bar shear cutting with numerical and experimental analysis. Bar shear cutting is an important operation because it precedes bulk metalworking processes for instance machining, extrusion and hot forging. In comparison to sheet shear cutting, bar shear cutting needs thermomechanical modelling. The variational formulation of the model is presented to predict damage mechanics in the bar shear cutting of aluminium alloys. Coupled thermomechanical modelling is required to analyse the mechanical behaviour of bulk workpieces, in which the combined effect of strain and temperature fields is considered in the shear cutting process. For this purpose, modified hardening and damage Johnson–Cook laws are developed. Numerical results for sheet and bar shear cutting operations are presented. The comparison betwee...

Accuracy of Variational Formulation to Model the Thermomechanical Problem and to Predict Failure in Metallic Materials

Mathematics

The main purpose of this study is to develop a variational formulation for predicting structure b... more The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting for damage mechanics in metallic materials. Mechanical and coupled thermomechanical models are used to predict failure in manufacturing processes. Ductile failure is accompanied by a significant amount of plastic deformation in metallic structural components. Finite element simulation of damage evolution in ductile solids is presented in this paper. Uncoupled models are implemented in a finite element model simulating deep drawing as well as cutting processes. Based on the Johnson–Cook model, the effect of deformation on the evolution of flow stress is described. The combined effect of strain, strain rate, and temperature on plasticity and damage behavior in cutting processes is considered. The accuracy of these models is verified when predicting ductile damage in forming and cutting processes.

Meshfree Analysis of 3-D Double Directors Shell Theory

Advances in Mechanical Engineering and Mechanics, 2019

A meshless implementation of arbitrary 3D-model based on a double directors shell element is deve... more A meshless implementation of arbitrary 3D-model based on a double directors shell element is developed in this work. The meshless technique is based on radial point interpolation method (RPIM) used for the construction of the shape functions for arbitrarily distributed nodes of the shell geometry. The high order shear deformation theory is adopted in this work in order to remove the shear correction coefficient. The convergence of the proposed model is compared to other well-known formulations found in the literature in order to outline the accuracy and performance of the present model.

Meshfree Modeling of 3D-Shell Structures Using the Modified First Order Shear Deformation Theory

Lecture Notes in Mechanical Engineering, 2020

This work develops a meshfree method for the analysis of 3D-shell structure based on the modified... more This work develops a meshfree method for the analysis of 3D-shell structure based on the modified first order shear deformation theory. The present meshfree method is based on the radial point interpolation method (RPIM) for the construction of the shape functions with Delta function property using arbitrarily distributed nodes in the support domains. The first order shear deformation theory is improved in this work in order to correct the constant shear strains with the Mindlin-Reissner theory and to get closer to its realistic distribution through the thickness with parabolic curves. The accuracy and convergence of the proposed model is compared to results presented in the literature.

Determination of Hyper-viscoelastic Parameters of Elastomeric Materials

Advances in Mechanical Engineering and Mechanics II, 2021

Finite Element Analysis of Nonlinear Behavior of FG Cantilever

Advances in Mechanical Engineering and Mechanics II, 2021

Experimental and numerical methodology to characterize 5083-aluminium behavior considering non-associated plasticity model coupled with isotropic ductile damage

International Journal of Solids and Structures, 2021

Abstract In the present work, an elastoplastic-damage model fully coupled with the constitutive e... more Abstract In the present work, an elastoplastic-damage model fully coupled with the constitutive equations of the non-associated plasticity is developed, to enrich the existing research results on the non-associated plasticity finite element models. The yield function and the plastic potential are represented independently by two different (Hill, 1948) quadratic functions to describe the anisotropic behavior of 5083-aluminium alloy. The current model develops a first attempt to establish a general formulation with two ductile degradation functions, one for elasticity and the other for plasticity, with variable degradation coefficients. Further, the elastoplastic behavior of 5083-aluminium alloy is determined through uniaxial tensile tests, so that the anisotropic, the isotropic hardening and the damage parameters are acquired. Experimental-numerical confrontation proves the reliability of the current formulation to describe the behavior of 5083-aluminium alloy with good accuracy. Furthermore, a novel numerical optimization procedure is firstly used to analytically identify Lemaitre damage parameters in order to limit the non-unicity of these parameters. The adopted optimization procedure offers a compromise between good accuracy and low computational time to determine the damage parameters.

An ABAQUS Implementation of a Solid-Shell Element: Application to Low Velocity Impact

Lecture Notes in Mechanical Engineering, 2020

The main objective of this work is to develop an hexahedral solid shell finite element in order t... more The main objective of this work is to develop an hexahedral solid shell finite element in order to resolve the numerical locking effects that may have occurred when employing the conventional solid and shell finite elements. The developed formulation relay on the coupling between the Assumed Natural Strain (ANS) and Enhanced Assumed Strain (EAS) methods. The FE model was implemented into the user element (UEL) interface of the FE commercial code ABAQUS by using the UEL FORTRAN subroutine. The robustness and performance of this element are proven using dynamic contact metal sheet behavior at low velocity impact. The obtained results are validated with finding from the literature. The developed solid shell element is efficient from a computational view point as the thickness direction is discretized adopting only single element layer.

Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method

Computers & Mathematics with Applications, 2020

Abstract This study conducts the first-known free vibration analysis of functionally graded carbo... more Abstract This study conducts the first-known free vibration analysis of functionally graded carbon nanotubes-reinforced (FG-CNTRC) shell structures using the meshfree radial point interpolation method (RPIM). The modified first-order shear deformation theory (modified FSDT) is implemented to get the realistic effect of the transverse shear deformation with its parabolic distribution. Numerical examples are carried out to examine the convergence and accuracy of the element-free RPIM method in its application to the free vibration FG-CNTRC analysis of shell structures. Results obtained using the proposed meshfree method, demonstrate that the improved FSDT is very successful compared to closed-form solutions and finite element results using different shell theories.

Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain

Engineering Computations, 2019

Purpose This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functi... more Purpose This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functionally graded shells using an efficient solid-shell element with parabolic transverse shear strain. Four different types of reinforcement along the thickness are considered. Design/methodology/approach Furthermore, the developed solid-shell element allows an efficient and accurate analysis of CNT-reinforced functionally graded shells under linear static conditions. Findings The validity and accuracy of the developed solid-shell element are illustrated through the solution of deflection and stress distribution problems of shell structures taken from the literature. The influences of some geometrical and material parameters on the static behavior of shell structures are discussed. Originality/value The finite element formulation is based on a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the ...

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Latin American Journal of Solids and Structures, 2017

In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is... more In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references.

Elasto-Plastic Modeling of Low-Velocity Impact on Functionally Graded Circular Plates

International Journal of Applied Mechanics, 2018

Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investig... more Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investigated in this paper based on Mori–Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the particle reinforced metal matrix FGM plate is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) and USDFLD subroutine. The effect of the power-law index on low-velocity impact parameters like contact force, deflection, permanent indentation, velocity distribution and the kinetic energy are examined using the proposed method. With the aim of demonstrating the accuracy and efficiency of the present method, current numer...

Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells

Engineering with Computers, 2018

A geometrically nonlinear analysis of elastoplastic ceramic/metal functionally graded material (F... more A geometrically nonlinear analysis of elastoplastic ceramic/metal functionally graded material (FGM) shells is investigated in this paper based on the first-order shear deformation theory. The elastoplastic behavior of the ceramic particle-reinforced metal matrix FGM shell is assumed to follow Ludwik hardening law. The elastoplastic material properties are assumed to vary smoothly through the thickness of the shells. The Mori-Tanaka model and self-consistent formulas of Suquet are employed to locally evaluate effective elastoplastic parameters of the ceramic/metal FGM composite. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) developed to study the FG shells in large displacements and rotations. With the aim of demonstrating the accuracy of the present method, current numerical results are compared to experimental and numerical ones considering geometrically nonlinear elastoplastic FGMs and show very good agreement. The overall robustness of the new developed solution taking into account both geometric and material nonlinearities is demonstrated through several non-trivial benchmark problems taken from the literature. The effect of the constituent distribution on the deflections is analyzed.

$Fig. 14 Elastoplastic and elastic deformed shapes of the FGM hyperboloid shell configuration for power law index p=10, U,: radial displace- ment It should pointed out that there are large differences between elastoplastic and elastic load—deflection curves. For the same load and the same volume fraction value, elastoplastic deflections are larger than elastic ones which is also illustrated also in Fig. 14, shown by elastoplastic and elastic deformed shapes of the FGM hyperboloid shell configuration for power law index p= 10. Those tests demonstrate the robustness of the present FEM using ABAQUS/UMAT and its applicability to arbi- trary shell geometries and coupled material and geometric nonlinearities. and elastic deformed shapes of the FGM hyperboloid shell$

An improved enhanced solid shell element for static and buckling analysis of shell structures

Mechanics & Industry, 2016

This paper presents an improved higher order solid shell element for static and buckling analysis... more This paper presents an improved higher order solid shell element for static and buckling analysis of laminated composite structures based on the enhanced assumed strain (EAS). The transverse shear strain is divided into two parts: the first one is independent of the thickness coordinate and formulated by the assumed natural strain (ANS) method; the second part is an enhancing part, which ensures a quadratic distribution through the thickness. This allows removing the shear correction factors and improves the accuracy of transverse shear stresses. In addition, volumetric locking is completely avoided by using the optimal parameters in the EAS method. The formulated finite element is implemented to study the static and buckling behavior of shell structures and to investigate the influence of some parameters on the buckling load. Comparisons of numerical results with those extracted from literature show the acceptable performance of the developed element.

Effects of the tool path strategies on incremental sheet metal forming process

Mechanics & Industry, 2016

This paper presents a numerical simulation of the incremental sheet metal forming (ISF) process, ... more This paper presents a numerical simulation of the incremental sheet metal forming (ISF) process, type single point incremental forming (SPIF). A finite element model (FEM) is developed by using the commercial FE code ABAQUS. An elasto-plastic constitutive model with quadratic yield criterion of Hill'48 and isotropic hardening behavior has been adopted during ISF operation. A user material subroutine (VUMAT) is used to implement this material behavior. Four strategies of tool path during the ISF of a piece having a square box final shape are presented. Results including thickness variation of sheet metal, forming force along Z-axis and the Hill'48 stress distribution for the four strategies are presented and compared at the aim to optimize the SPIF and to see which tool path strategy makes this process more effective with the consideration of the characteristics of specimen manufactured and its material properties.

Fatigue Behavior of Short Glass Fiber Reinforced Polyamide 66: Experimental Study and Fatigue Damage Modelling

Periodica Polytechnica Mechanical Engineering, 2016

The aim of the present paper is to study and model the fatigue behavior of short glass fibers rei... more The aim of the present paper is to study and model the fatigue behavior of short glass fibers reinforced polyamide-66. The effect of fiber content on the fatigue and static behavior of this composite is investigated. In such composites fatigue damage growth exhibits three stages. A continuum damage based model is presented to predict damage evolution during these three stages. Experimental results show that increasing the fiber content increases the elastic modulus and the tensile strength of the studied materials under tensile tests. However, the rupture behavior changes from ductile to brittle. Moreover increasing the fiber percentage changes the S-N curves slope and decreases the fatigue life. Analytical results predicted by the proposed model, compared to experimental ones shows good agreement and the developed model predicted fatigue damage growth in its three stages of evolution with good performance.

$The specimen behavior exhibits three distinct stages of stiff- ness degradation during displacement controlled bending fatigue tests: (i) The first stage shows rapid stiffness reduction caused by the development of matrix micro-voids; (11) In the second stage, the dominant damage mechanisms are coalescence and propagation of the micro-cracks. A gradual stiffness reduction of the material occurs in an approximately linear manner. The majority of fatigue life is categorized under this region. (iii) The last stage is characterized by sudden stiffness reduction fol- lowed by total failure. The most dominant failure in this region is fiber fracture and macroscopic crack propagation [14, 31]. The evolution of the maximum induced stress acting in the composite specimen versus the number of cycles is shown in Fig. 11 and 12 using logarithmic scale. The higher applied displacement is the higher the initial force acting in the com- posite specimen. The curves display three stages: The first stage is characterized by a decrease of the material rigidity The evolution of the maximum induced stress acting in the last stage is characterized by sudden stiffness reduction fol-$

Finite element implementation of an orthotropic plasticity model for sheet metal in low velocity impact simulations

Thin-Walled Structures, 2015

A finite element (FE) implementation of an orthotropic plasticity model for sheet metal in impact... more A finite element (FE) implementation of an orthotropic plasticity model for sheet metal in impact simulations is performed. An accurate description of anisotropic plasticity model is presented for obtaining reliable predictions in FE simulations of low velocity impact processes. The elasto-plastic model includes isotropic elasticity, anisotropic yielding, associated plastic flow and mixed non-linear isotropic/kinematic hardening. The material model is implemented into a user-defined material (VUMAT) subroutine for the commercial finite element code ABAQUS/Explicit to predict the numerical response of circular aluminum plate subjected to low velocity impact. The impact energy was imposed by the definition of the impactor initial velocity. The numerical results of the impact force history and impact velocity are in good agreements with the LDA experimental data. The anisotropy effect of aluminum plate under low velocity impact is studied.

FGM Shell Structures Analysis Using an Enhanced Discrete Double Directors Shell Element

Lecture Notes in Mechanical Engineering, 2014

ABSTRACT In order to examine the accuracy of the enhanced double directors shell model for the fu... more ABSTRACT In order to examine the accuracy of the enhanced double directors shell model for the functionally graded material (FGM) shell structures, a series of benchmark static tests are tackled using finite elements method. For implementing the discrete double directors shell model (DDDSM) within the Enhanced Strain Technique (EST), four parameters are used for enhancing the membrane strain. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. The mechanical properties of the shell structure are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. A comparison with the exact solutions presented by several authors for shell structures indicates that the present model accurately estimates the stress-strain responses.

Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

This paper is focused on the structural shape optimization of incompressible hyperelastic structu... more This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.

Numerical Formulation of Anisotropic Elastoplastic Behavior Coupled with Damage Model in Forming Processes

Mathematics

The present paper proposes a mathematical development of the plasticity and damage approaches to ... more The present paper proposes a mathematical development of the plasticity and damage approaches to simulate sheet metal forming processes. It focuses on the numerical prediction of the deformation of the sheet metal during the deep drawing process when a crack appears. Anisotropic plasticity constitutive equations are proposed. A fully implicit integration of the coupling constitutive equations is used and leads to two nonlinear local scalar equations that are solved by Newton’s method. The developed model allows predicting the onset of cracks in sheet metals during cold forming operations. The numerical model is implemented in ABAQUS software using user-defined subroutines, which are VUMAT and UMAT. The accuracy of the anisotropic elastoplastic model fully coupled with ductile damage is evaluated using numerical examples.

Mathematical Model Describing the Hardening and Failure Behaviour of Aluminium Alloys: Application in Metal Shear Cutting Process

Mathematics

Recent research has focused on sheet shear cutting operations. However, little research has been ... more Recent research has focused on sheet shear cutting operations. However, little research has been conducted on bar shear cutting. The main objective of the present investigation is to study bar shear cutting with numerical and experimental analysis. Bar shear cutting is an important operation because it precedes bulk metalworking processes for instance machining, extrusion and hot forging. In comparison to sheet shear cutting, bar shear cutting needs thermomechanical modelling. The variational formulation of the model is presented to predict damage mechanics in the bar shear cutting of aluminium alloys. Coupled thermomechanical modelling is required to analyse the mechanical behaviour of bulk workpieces, in which the combined effect of strain and temperature fields is considered in the shear cutting process. For this purpose, modified hardening and damage Johnson–Cook laws are developed. Numerical results for sheet and bar shear cutting operations are presented. The comparison betwee...

Accuracy of Variational Formulation to Model the Thermomechanical Problem and to Predict Failure in Metallic Materials

Mathematics

The main purpose of this study is to develop a variational formulation for predicting structure b... more The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting for damage mechanics in metallic materials. Mechanical and coupled thermomechanical models are used to predict failure in manufacturing processes. Ductile failure is accompanied by a significant amount of plastic deformation in metallic structural components. Finite element simulation of damage evolution in ductile solids is presented in this paper. Uncoupled models are implemented in a finite element model simulating deep drawing as well as cutting processes. Based on the Johnson–Cook model, the effect of deformation on the evolution of flow stress is described. The combined effect of strain, strain rate, and temperature on plasticity and damage behavior in cutting processes is considered. The accuracy of these models is verified when predicting ductile damage in forming and cutting processes.

Meshfree Analysis of 3-D Double Directors Shell Theory

Advances in Mechanical Engineering and Mechanics, 2019

A meshless implementation of arbitrary 3D-model based on a double directors shell element is deve... more A meshless implementation of arbitrary 3D-model based on a double directors shell element is developed in this work. The meshless technique is based on radial point interpolation method (RPIM) used for the construction of the shape functions for arbitrarily distributed nodes of the shell geometry. The high order shear deformation theory is adopted in this work in order to remove the shear correction coefficient. The convergence of the proposed model is compared to other well-known formulations found in the literature in order to outline the accuracy and performance of the present model.

Meshfree Modeling of 3D-Shell Structures Using the Modified First Order Shear Deformation Theory

Lecture Notes in Mechanical Engineering, 2020

This work develops a meshfree method for the analysis of 3D-shell structure based on the modified... more This work develops a meshfree method for the analysis of 3D-shell structure based on the modified first order shear deformation theory. The present meshfree method is based on the radial point interpolation method (RPIM) for the construction of the shape functions with Delta function property using arbitrarily distributed nodes in the support domains. The first order shear deformation theory is improved in this work in order to correct the constant shear strains with the Mindlin-Reissner theory and to get closer to its realistic distribution through the thickness with parabolic curves. The accuracy and convergence of the proposed model is compared to results presented in the literature.

Determination of Hyper-viscoelastic Parameters of Elastomeric Materials

Advances in Mechanical Engineering and Mechanics II, 2021

Finite Element Analysis of Nonlinear Behavior of FG Cantilever

Advances in Mechanical Engineering and Mechanics II, 2021

Experimental and numerical methodology to characterize 5083-aluminium behavior considering non-associated plasticity model coupled with isotropic ductile damage

International Journal of Solids and Structures, 2021

Abstract In the present work, an elastoplastic-damage model fully coupled with the constitutive e... more Abstract In the present work, an elastoplastic-damage model fully coupled with the constitutive equations of the non-associated plasticity is developed, to enrich the existing research results on the non-associated plasticity finite element models. The yield function and the plastic potential are represented independently by two different (Hill, 1948) quadratic functions to describe the anisotropic behavior of 5083-aluminium alloy. The current model develops a first attempt to establish a general formulation with two ductile degradation functions, one for elasticity and the other for plasticity, with variable degradation coefficients. Further, the elastoplastic behavior of 5083-aluminium alloy is determined through uniaxial tensile tests, so that the anisotropic, the isotropic hardening and the damage parameters are acquired. Experimental-numerical confrontation proves the reliability of the current formulation to describe the behavior of 5083-aluminium alloy with good accuracy. Furthermore, a novel numerical optimization procedure is firstly used to analytically identify Lemaitre damage parameters in order to limit the non-unicity of these parameters. The adopted optimization procedure offers a compromise between good accuracy and low computational time to determine the damage parameters.

An ABAQUS Implementation of a Solid-Shell Element: Application to Low Velocity Impact

Lecture Notes in Mechanical Engineering, 2020

The main objective of this work is to develop an hexahedral solid shell finite element in order t... more The main objective of this work is to develop an hexahedral solid shell finite element in order to resolve the numerical locking effects that may have occurred when employing the conventional solid and shell finite elements. The developed formulation relay on the coupling between the Assumed Natural Strain (ANS) and Enhanced Assumed Strain (EAS) methods. The FE model was implemented into the user element (UEL) interface of the FE commercial code ABAQUS by using the UEL FORTRAN subroutine. The robustness and performance of this element are proven using dynamic contact metal sheet behavior at low velocity impact. The obtained results are validated with finding from the literature. The developed solid shell element is efficient from a computational view point as the thickness direction is discretized adopting only single element layer.

Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method

Computers & Mathematics with Applications, 2020

Abstract This study conducts the first-known free vibration analysis of functionally graded carbo... more Abstract This study conducts the first-known free vibration analysis of functionally graded carbon nanotubes-reinforced (FG-CNTRC) shell structures using the meshfree radial point interpolation method (RPIM). The modified first-order shear deformation theory (modified FSDT) is implemented to get the realistic effect of the transverse shear deformation with its parabolic distribution. Numerical examples are carried out to examine the convergence and accuracy of the element-free RPIM method in its application to the free vibration FG-CNTRC analysis of shell structures. Results obtained using the proposed meshfree method, demonstrate that the improved FSDT is very successful compared to closed-form solutions and finite element results using different shell theories.

Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain

Engineering Computations, 2019

Purpose This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functi... more Purpose This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functionally graded shells using an efficient solid-shell element with parabolic transverse shear strain. Four different types of reinforcement along the thickness are considered. Design/methodology/approach Furthermore, the developed solid-shell element allows an efficient and accurate analysis of CNT-reinforced functionally graded shells under linear static conditions. Findings The validity and accuracy of the developed solid-shell element are illustrated through the solution of deflection and stress distribution problems of shell structures taken from the literature. The influences of some geometrical and material parameters on the static behavior of shell structures are discussed. Originality/value The finite element formulation is based on a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the ...

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Latin American Journal of Solids and Structures, 2017

In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is... more In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references.

Elasto-Plastic Modeling of Low-Velocity Impact on Functionally Graded Circular Plates

International Journal of Applied Mechanics, 2018

Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investig... more Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investigated in this paper based on Mori–Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the particle reinforced metal matrix FGM plate is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) and USDFLD subroutine. The effect of the power-law index on low-velocity impact parameters like contact force, deflection, permanent indentation, velocity distribution and the kinetic energy are examined using the proposed method. With the aim of demonstrating the accuracy and efficiency of the present method, current numer...

Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells

Engineering with Computers, 2018

A geometrically nonlinear analysis of elastoplastic ceramic/metal functionally graded material (F... more A geometrically nonlinear analysis of elastoplastic ceramic/metal functionally graded material (FGM) shells is investigated in this paper based on the first-order shear deformation theory. The elastoplastic behavior of the ceramic particle-reinforced metal matrix FGM shell is assumed to follow Ludwik hardening law. The elastoplastic material properties are assumed to vary smoothly through the thickness of the shells. The Mori-Tanaka model and self-consistent formulas of Suquet are employed to locally evaluate effective elastoplastic parameters of the ceramic/metal FGM composite. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) developed to study the FG shells in large displacements and rotations. With the aim of demonstrating the accuracy of the present method, current numerical results are compared to experimental and numerical ones considering geometrically nonlinear elastoplastic FGMs and show very good agreement. The overall robustness of the new developed solution taking into account both geometric and material nonlinearities is demonstrated through several non-trivial benchmark problems taken from the literature. The effect of the constituent distribution on the deflections is analyzed.

$Fig. 14 Elastoplastic and elastic deformed shapes of the FGM hyperboloid shell configuration for power law index p=10, U,: radial displace- ment It should pointed out that there are large differences between elastoplastic and elastic load—deflection curves. For the same load and the same volume fraction value, elastoplastic deflections are larger than elastic ones which is also illustrated also in Fig. 14, shown by elastoplastic and elastic deformed shapes of the FGM hyperboloid shell configuration for power law index p= 10. Those tests demonstrate the robustness of the present FEM using ABAQUS/UMAT and its applicability to arbi- trary shell geometries and coupled material and geometric nonlinearities. and elastic deformed shapes of the FGM hyperboloid shell$

An improved enhanced solid shell element for static and buckling analysis of shell structures

Mechanics & Industry, 2016

This paper presents an improved higher order solid shell element for static and buckling analysis... more This paper presents an improved higher order solid shell element for static and buckling analysis of laminated composite structures based on the enhanced assumed strain (EAS). The transverse shear strain is divided into two parts: the first one is independent of the thickness coordinate and formulated by the assumed natural strain (ANS) method; the second part is an enhancing part, which ensures a quadratic distribution through the thickness. This allows removing the shear correction factors and improves the accuracy of transverse shear stresses. In addition, volumetric locking is completely avoided by using the optimal parameters in the EAS method. The formulated finite element is implemented to study the static and buckling behavior of shell structures and to investigate the influence of some parameters on the buckling load. Comparisons of numerical results with those extracted from literature show the acceptable performance of the developed element.

Effects of the tool path strategies on incremental sheet metal forming process

Mechanics & Industry, 2016

This paper presents a numerical simulation of the incremental sheet metal forming (ISF) process, ... more This paper presents a numerical simulation of the incremental sheet metal forming (ISF) process, type single point incremental forming (SPIF). A finite element model (FEM) is developed by using the commercial FE code ABAQUS. An elasto-plastic constitutive model with quadratic yield criterion of Hill'48 and isotropic hardening behavior has been adopted during ISF operation. A user material subroutine (VUMAT) is used to implement this material behavior. Four strategies of tool path during the ISF of a piece having a square box final shape are presented. Results including thickness variation of sheet metal, forming force along Z-axis and the Hill'48 stress distribution for the four strategies are presented and compared at the aim to optimize the SPIF and to see which tool path strategy makes this process more effective with the consideration of the characteristics of specimen manufactured and its material properties.

Fatigue Behavior of Short Glass Fiber Reinforced Polyamide 66: Experimental Study and Fatigue Damage Modelling

Periodica Polytechnica Mechanical Engineering, 2016

The aim of the present paper is to study and model the fatigue behavior of short glass fibers rei... more The aim of the present paper is to study and model the fatigue behavior of short glass fibers reinforced polyamide-66. The effect of fiber content on the fatigue and static behavior of this composite is investigated. In such composites fatigue damage growth exhibits three stages. A continuum damage based model is presented to predict damage evolution during these three stages. Experimental results show that increasing the fiber content increases the elastic modulus and the tensile strength of the studied materials under tensile tests. However, the rupture behavior changes from ductile to brittle. Moreover increasing the fiber percentage changes the S-N curves slope and decreases the fatigue life. Analytical results predicted by the proposed model, compared to experimental ones shows good agreement and the developed model predicted fatigue damage growth in its three stages of evolution with good performance.

$The specimen behavior exhibits three distinct stages of stiff- ness degradation during displacement controlled bending fatigue tests: (i) The first stage shows rapid stiffness reduction caused by the development of matrix micro-voids; (11) In the second stage, the dominant damage mechanisms are coalescence and propagation of the micro-cracks. A gradual stiffness reduction of the material occurs in an approximately linear manner. The majority of fatigue life is categorized under this region. (iii) The last stage is characterized by sudden stiffness reduction fol- lowed by total failure. The most dominant failure in this region is fiber fracture and macroscopic crack propagation [14, 31]. The evolution of the maximum induced stress acting in the composite specimen versus the number of cycles is shown in Fig. 11 and 12 using logarithmic scale. The higher applied displacement is the higher the initial force acting in the com- posite specimen. The curves display three stages: The first stage is characterized by a decrease of the material rigidity The evolution of the maximum induced stress acting in the last stage is characterized by sudden stiffness reduction fol-$

Finite element implementation of an orthotropic plasticity model for sheet metal in low velocity impact simulations

Thin-Walled Structures, 2015

A finite element (FE) implementation of an orthotropic plasticity model for sheet metal in impact... more A finite element (FE) implementation of an orthotropic plasticity model for sheet metal in impact simulations is performed. An accurate description of anisotropic plasticity model is presented for obtaining reliable predictions in FE simulations of low velocity impact processes. The elasto-plastic model includes isotropic elasticity, anisotropic yielding, associated plastic flow and mixed non-linear isotropic/kinematic hardening. The material model is implemented into a user-defined material (VUMAT) subroutine for the commercial finite element code ABAQUS/Explicit to predict the numerical response of circular aluminum plate subjected to low velocity impact. The impact energy was imposed by the definition of the impactor initial velocity. The numerical results of the impact force history and impact velocity are in good agreements with the LDA experimental data. The anisotropy effect of aluminum plate under low velocity impact is studied.

FGM Shell Structures Analysis Using an Enhanced Discrete Double Directors Shell Element

Lecture Notes in Mechanical Engineering, 2014

ABSTRACT In order to examine the accuracy of the enhanced double directors shell model for the fu... more ABSTRACT In order to examine the accuracy of the enhanced double directors shell model for the functionally graded material (FGM) shell structures, a series of benchmark static tests are tackled using finite elements method. For implementing the discrete double directors shell model (DDDSM) within the Enhanced Strain Technique (EST), four parameters are used for enhancing the membrane strain. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. The mechanical properties of the shell structure are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. A comparison with the exact solutions presented by several authors for shell structures indicates that the present model accurately estimates the stress-strain responses.

Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

This paper is focused on the structural shape optimization of incompressible hyperelastic structu... more This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.