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This research makes a first attempt to investigate the dynamic characteristics of functionally graded carbon nanotube–reinforced composite plates and shell structures with surface-bonded piezoelectric layers. A variational formulation is derived based on the linear double director shell theory to ensure realistic parabolic variation of transverse shear strain along the thickness direction. The assumed natural strains method is adopted to enhance the accuracy of the four-node piezoelectric shell element developed in this study. Numerical studies are conducted to validate the efficiency and numerical stability of the proposed model to predict the behavior of piezolaminated composite shell structures. Furthermore, dynamic responses are extended to functionally graded carbon nanotube–reinforced composite shells covered by two active layers. The host structure is reinforced by single-walled carbon nanotubes, which are assumed to be graded through the thickness direction with different types of distributions and embedded in a polymer matrix. The effect of the volume fractions, distribution type, and geometrical parameters of the carbon nanotubes is examined.

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 compatible strain part. This formulation guarantees a zero transverse shear stress on the top and bottom surfaces of the shell and the shear correction factors is no longer needed.

In the present paper, as a first endeavor, homogenization of elasto-plastic functionally graded material (FGM) is investigated based on representative volume element (RVE) and used for the first time in the single point incremental forming (SPIF) process. The effective properties of elasto-plastic spheres-reinforced FGM composite are determined using the numerical RVE method and Mori-Tanaka model. In order to implement the homogenization equations and numerical algorithm into Abaqus Software, user-defined material, (VUMAT) and (VUSFLD) subroutines are employed. The accuracy of the proposed homogenization methodology is highlighted through comparisons of the present results with those taken from the literature and an excellent agreement is found. During SPIF process, the effect of the power-law index on the formability, plastic deformation, forming force along Z_direction and Von Mises distribution is analyzed. Parametric studies are conducted to show the influence of cone wall angle and sheet thickness on the formability and the thinning along the SPIF process.

This paper presents a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the compatible strain part. Moreover, zero transverse shear stress on the top and bottom surfaces of the shell is satisfied exactly and the shear correction factors is no longer needed. Furthermore, the developed solid-shell element allows an efficient and accurate analysis of functionally graded material shells under geometric nonlinear static conditions. A simple power-law functionally graded distribution of the shells along the thickness direction is considered. The validity and accuracy of the developed solid-shell element are illustrated through the solution of several known problems taken from the literature. The influences of power-law index on the nonlinear static behavior of the FGM shells are discussed.

The purpose of the paper is to predict the electromechanical behavior of composite shell structures with embedded piezoelectric layers using 3D-shell model based on a discrete double directors shell element. The implementation is applicable to the analysis of isotropic and functionally graded shells with integrated piezoelectric layers. The third-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The present results were compared with reference solutions from literature in order to verify the accuracy of the present formulation and excellent agreement was found. A parametric study is carried out to highlight the influence of material composition and curvature radius on the deflection and axial stress along the thickness.

A meshfree analysis of arbitrary 3D-model based on a double directors shell model is first investigated in this paper. The high order shear deformation theory is implemented in the present work in order to remove the shear correction coefficient. The radial point interpolation method is used in the construction of shape functions based on arbitrarily distributed nodes of general spatial shell geometry. Discrete system of equations is obtained by incorporating these interpolations into the weak form. The formulation is tested on several benchmark problems considering isotropic and functionally graded spatial shell structures. Numerical tests show that the method is reliable, robust and produces accurate results compared to closed-form solutions and finite element results. The effect of the material distribution on the deflections and stresses is analyzed.

This article investigates geometrically nonlinear and linear analysis of multilayered shells with integrated piezoelectric materials. An efficient nonlinear shell element is developed to solve piezoelastic response of laminated structure with embedded piezoelectric actuators and sensors. A modified first-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The electric potential is assumed to be a linear function through the thickness of each active sub-layer. Several numerical tests for different piezolaminated geometries are conducted to highlight the reliability and efficiency of the proposed implementation in linear and geometrically nonlinear finite element analysis.

In this paper, an improved anisotropic elasto-plastic model strongly coupled with isotropic ductile damage is investigated. The quadratic Hill’48 yield criterion and non-linear isotropic/kinematic hardening are considered in the associated flow rule model. The numerical formulation of the proposed model is implemented in ABAQUS finite element code via the user material subroutines UMAT and VUMAT. The mechanical behavior of DD13 sheet metal is investigated. Its significant deep drawing capability makes this material attractive, particularly for the automotive industry. An experimental database of the DD13 mechanical properties is achieved through a serie of uniaxial tensile tests, so that the anisotropic coefficients, hardening and damage parameters are obtained. For validation purpose, the numerical results are compared to Erichsen cupping test. The combined experimental/numerical study proves the ability of the proposed model in the description of the DD13 damaged-anisotropic behavior with good accuracy.

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.

A numerical study was carried out to investigate the low velocity impact behavior of polyamide (PA) as matrix reinforced by a glass fiber. The assessment of the impact behavior requires tensile tests to determine the elastic-viscoplastic behavior of the composites. The numerical results are confirmed by experimental dropping weight impact tests. The material model is implemented in a user-defined material subroutine (UMAT) for the commercial finite element code ABAQUS to predict the numerical response of circular plate of glass fiber-reinforced polyamide subjected to low velocity impact. The effects of glass fiber volume fraction and incidental impact energy on the impact response of the composite circular plates are investigated. The impact analysis of the glass fiber-reinforced polyamide showed that the impactor velocity has considerable effects on the impact response of the composite plates. Also, the contact force changes proportionally with the impactor velocity.

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.

The purpose of this paper is to study numerically the “elastomer-assisted compression beading” (EACB process). It consists of conventional compressing beading after a local bulging carried out by an elastomer material. A Finite Element Method (FEM) is introduced to predict where and when the damage can occur in the tube and to study the effects of anisotropy on the occurrence of failure by cracking in regions where damage is accumulated. An anisotropic elasto-plastic constitutive model with mixed non-linear isotropic/kinematic hardening fully coupled with Lemaitre's ductile damage is implemented in ABAQUS/Explicit software via VUMAT subroutine. The influence of anisotropy on the damage evolution is investigated in this study and results are compared with isotropic model.

The incremental sheet forming (ISF) is a flexible forming technology in the sheet metal engineering. This process reaches a higher formability of manufactured sheets than conventional sheet metal stamping process. A deep insight into parameters influencing this process is crucial for more understanding of the process. This paper presents a numerical investigation of damage mechanism during the Single Point Incremental sheet metal Forming (SPIF) of a part with conical shape. An elasto-plastic constitutive model with quadratic yield criteria of Hill’48 and mixed isotropic/kinematic hardening behavior is adopted to simulate ISF operation. A user material subroutine (VUMAT) is employed to implement the material behavior of the sheet metal. The efficiency of the finite element model to predict the material deformation process is investigated by comparing numerical and experimental results. A comparison between two hardening models in terms of deformed shape after springback and thickness evolution is presented. Damage evolution is investigated by comparing the results of two hardening models. The final part is devoted to study the influence of some process parameters on the damage evolution and forming effort during the SPIF of studied parts.

This paper deals with the implementation of an anisotropic plasticity constitutive equations exhibiting non-linear isotropic, kinematic hardening and coupled continuum ductile damage models. A fully implicit integration of the coupling constitutive equations is adopted and leads to two non-linear local scalar equations solved using the Newton method. The consistent local tangent modulus is obtained in a closed form by exact linearization of the algorithm. The numerical treatment of the proposed algorithm is implemented on ABAQUS using user interface material subroutines (UMAT and VUMAT). The performance of the present algorithm is assessed and bared out by numerical examples.

A finite element simulation of flexible bulge forming of aluminum sheet metal is carried out. The effect of rubber pad on forming capability is studied by comparing flexible bulge to hydroforming. Based on the theory of Continuum Damage Mechanics (CDM), a local approach with fully coupling between ductile damage and an anisotropic elasto-plastic model with mixed nonlinear kinematic/isotropic hardening is introduced. The model is implemented into a user-defined material (VUMAT) subroutine for the commercial finite element code ABAQUS/Explicit. A Mooney-Rivlin theory is adopted for rubber material behavior. Comparisons between both processes in terms of thickness variation, damage occurrence, and sheet formability are conducted for different rubber shores and friction. Numerical findings are in a good correlation with experiments from literature.

A numerical investigation was carried out to analyze in details the perforation process of target AA5754-O Aluminum plate when subjected to normal impact at low (up to 25 ms − 1 ) and moderate velocities (ranged between 25 − 50 ms − 1 ). A fully coupled elasto-visco-plastic-damage model is implemented into a user-defined material (VUMAT) subroutine for the commercial finite element code ABAQUS/Explicit. The strain rate effect is considered. Comparison between isotropic J 2 and orthotropic Hill yield criteria associated with isotropic and mixed non-linear isotropic/kinematic hardening was conducted. A parametric study of the effect of anisotropy, plate thickness and impactor nose shapes on ballistic limit and petal forming is carried out. A good agreement is found between numerical and experimental results conducted by other researchers.

This paper presents a 2-node, 4 DOF/node beam element based on higher order shear deformation theory for axial–flexural-shear functionally graded material. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the beam. A discrete constraint is used to get the stress free condition on the top and bottom surface and to avoid the C1 transverse continuous displacement. A beam element, based on a displacement formulation, is first developed. Next, the numerical treatment of the shear field is improved in a second element using a mixed formulation. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of mixed beam element and the reference solutions. The proposed formulation gives an exact solution at the nodes even for a coarse mesh.

Rubber forming is a sheet metal forming process using flexible punch or die. In this paper, finite element method is introduced to analyze rubber-pad forming process of aluminum sheet metal. An elasto-plastic constitutive model with J 2 yield criterion and mixed non-linear isotropic/kinematic hardening coupled with Lemaitre's ductile damage has been adopted during flexible forming operation. To model rubber material, a Mooney-Rivlin theory is used in the finite element simulation. A stamping of aluminum sheet metal with soft punch is simulated. A fully coupled elasto-plastic damage model is implemented in ABAQUS/Standard software via UMAT subroutine to study the effect of some key process parameters like hardness of rubber, type of rubber on the variation of the thickness, the springback and damage of aluminum sheet metal.

The purpose of the paper is to compute the dynamic behavior of functionally graded material (FGM) shell structures subjected to time-varying excitation using 3D-shell model based on a discrete double directors shell element. The third-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. Material properties of the shell are assumed to be graded in the thickness direction by varying the volume fraction of the ceramic and the metallic constituents using general four-parameter power-law distribution. The transient excitation is defined in the time domain and known at each time. The damping material is neglected and the time derivative is approximated by Newmark method. Numerical results for deflection and stresses are presented for plates and spherical caps. The effect of an imposed force on the response of the FGM shell is discussed. The numerical examples prove a good accuracy and reliability compared to the few results available in literature.

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 present paper describes the development of a unified hyperelastic constitutive model based on anisotropic hyperelastic material with families of fibers approach and integrating both; pure isotropic matrix of polyamide-6.6 and anisotropic materials induced by the short glass fiber reinforcement (SGFR), into one framework. The material model is implemented in a four-node shell element. The model is used to predict the mechanical behavior of SGFR polyamide-6.6. Material parameters are identified using experimental data from tensile tests on unreinforced and 10, 20, and 30% wt reinforced, polyamide-6.6. The proposed model is validated with two points bending experimental results. Experimental and finite elements results are compared. Numerical results prove the good performances of the developed model to predict the anisotropic behavior of SGFR polyamide-6.6.

In this paper, non-linear dynamics analysis of functionally graded material (FGM) shell structures is investigated using the higher order solid-shell element based on the Enhanced Assumed Strain (EAS). With this element, a quadratic distribution of the shear stress through the thickness is considered in an enhancing part. Material properties of the shell structure are varied continuously in the thickness direction according to the general four-parameter power-law distribution in terms of the volume fractions of the constituents. Performance and accuracy of the present higher order solid-shell element are confirmed by comparing the numerical results obtained from finite element analyses with results from the literature.

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 numerical results are compared to experimental and theoretical results from the literature and show very good agreement.

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.

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.

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.