Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

Three-dimensional stress and progressive failure analysis of ultra thick laminates and experimental validation

Test methods and analysis capabilities for fibre reinforced composites are generally limited to thin laminates. However, extending the range of application of composite materials to thick laminates is essential for a multitude of possible composite structures. This paper presents an adapted three-point bending test for a new quasi isotropic stacking sequence for non crimped fabrics for the application in ultra thick laminates (UTL). In addition, numerical simulation capabilities for thick laminates using a multiscale analysis are shown. The three-point bending test setup is developed to examine the failure behaviour of 30–60 mm thick coupons.     

Multiscale finite element modeling of superelasticity in Nitinol polycrystals

An efficient method is proposed for modeling superelastic polycrystalline NiTi by solving a two-scale problem. The RVE size of the fine scale is determined using a statistics-based approach. Both problems are discretized in space using the finite element method and their communication is effected using MPI. Representative simulations illustrate the modeling capabilities of the proposed approach.     

基于有限元和神经网络的杂交建模

针对复杂非线性结构动力学系统提出了一种基于有限元与神经网络相结合的杂交建模方法。依据该方法,首先将系统中的线性结构部分采用有限元建模,非线性或难以机理建模的结构部件采用神经网络描述。其次,再通过力和位移边界联接条件将有限元模型部分和神经网络模型部分结合从而得到整个系统的杂交模型,且杂交模型的物理结构明确,精度较高,网络规模较小。在一非线性隔振系统的杂交建模算例仿真中,用所建杂交模型对正弦及宽带随机激励进行了预测检验分析,结果良好,该杂交建模方法为主体结构为线弹性结构而又包含有强非线性器件的非线性动力学系统提供了一种有效的建模途径。     

A micromechanical composite approach for finite element crashworthiness simulation

The present article deals with micromechanical composite modeling. Both analytical and computational micromechanics approaches are described as well as micromechanical modeling of damage. Based on micromechanics of failure theory, a user subroutine including a progressive damage algorithm is programmed for finite element analysis. Three theory-experiment correlations of tubes under a three-point bending test have been carried out using the bi-phase material model developed along with this project. These studies include three-ply schedules.     

Nonlinear failure prediction of concrete composite columns by a mixed finite element formulation

This study focuses on developing a mixed frame finite element formulation of reinforced concrete and FRP composite columns in order to give more accuracy not only to predict the global behavior of the structural system but also to predict the local damage in the cross-section. A hypo-elastic constitutive law of concrete is presented under the basis of a three-dimensional stress state in order to model the compressive behavior of confined concrete wrapped with FRP jackets. To predict the nonlinear load path-dependent confinement model of FRP-confined concrete, the strength enhancement of concrete was determined by the failure surface of concrete in a tri-axial stress state, and its corresponding peak strain was computed by the strain-enhancement factor proposed in this study. The behavior of FRP jacket was modeled using the two-dimensional classical lamination theory. The flexural behavior of concrete and composite members was defined using a nonlinear fiber cross-sectional approach. The results obtained by developed mixed finite element formulation were verified with the experiments of concrete composite columns and also were compared with a displacement-based finite element formulation. It is shown that the proposed formulation gives e more accurate results in the global behavior of the column system as well as in the local damage in the column sections.     

Parametric study of stress state development during twinning using 3D finite element modeling

A deformation twinning model which simulates the characteristic twin shear and corresponding grain reorientation has been developed using a 3D finite element method. This model has been used to study how twinning affects the stress state in both the parent grain and twin, and the stress states that are energetically favorable for twinning. The component of shear stress on the twin plane and direction is primarily responsible not only for whether twinning can occur, but also the energetically favorable twin volume fraction. A map predicting twin volume fraction as a function of parent grain deviatoric stress has been developed.     

Free vibration of composite and sandwich laminates with a higher-order facet shell element

A simple C⁰ isoparametric finite element formulation based on a shear deformable model of higher-order theory using a higher-order facet shell element is presented for the free vibration analysis of isotropic, orthotropic and layered anisotropic composite and sandwich laminates. This theory incorporates a realistic non-linear variation of displacements through the shell thickness, and eliminates the use of shear correction coefficients. The validity and efficiency of the present formulation is established by obtaining solutions to a wide range of problems and comparing them with the available three-dimensional closed-form and finite element solutions. In addition, other plate and shell solutions of different kind and available in the literature are also compiled and tabulated for the sake of completeness. The parametric effects of degree of orthotropy, length-to-thickness ratio, plate aspect ratio, number of layers and fibre orientation upon the frequencies and mode shapes are discussed.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.     

Stochastic progressive failure analysis of laminated composite plates using Puck's failure criteria

The present work deals with second-order statistics of the progressive failure response of laminated composite plates subjected to in-plane uniaxial and bi-axial loadings with random system properties. A stochastic finite element method based on higher-order shear deformation theory combined with first- and second-order perturbation technique is used for solution of random progressive failure equation. A Puck failure criterion is used for the evaluation of first ply and last-ply failure load. The results obtained using the present solution approach are validated with the results available in the literature and Monte Carlo simulation.     

Coupled finite element simulation and optimization of single- and multi-stage sheet-forming processes

This article presents the development and application of a coupled finite element simulation and optimization framework that can be used for design and analysis of sheet-forming processes of varying complexity. The entire forming process from blank gripping and deep drawing to tool release and springback is modelled. The dies, holders, punch and workpiece are modelled with friction, temperature, holder force and punch speed controlled in the process simulation. Both single- and multi-stage sheet-forming processes are investigated. Process simulation is coupled with a nonlinear gradient-based optimization approach for optimizing single or multiple design objectives with imposed sheet-forming response constraints. A MATLAB program is developed and used for data-flow management between process simulation and optimization codes. Thinning, springback, damage and forming limit diagram are used to define failure in the forming process design optimization. Design sensitivity analysis and optimization results of the example problems are presented and discussed.     

再生塑料内污染物迁移的有限元分析

建立计算仿真模型,该模型可用来预测再生塑料内污染物向液体产品(如食品)的迁移.该仿真模型的建立是基于有限元方法,可分析多层结构中的迁移.该项工作对于再生塑料尤其是有低阻隔性的聚烯烃在食品包装上的应用具有潜在意义.     

Micromechanics modeling of fatigue failure mechanisms in a hybrid polymer matrix composite

Initiation of fatigue damage for a hybrid polymer matrix composite material was studied via 3-Dimensional viscoelastic representative volume element modeling in order to gain further understanding. It was found that carbon fiber reinforced composites perform better in fatigue loading, in comparison to glass fiber reinforced composites, due to the fact that the state of stress within the matrix material was considerably lower for carbon fiber reinforced composites eliminating (or at least prolonging) fatigue damage initiation. The effect of polymer aging was also evaluated through thermal aging of neat resin specimens. Short-term viscoelastic material properties of unaged and aged neat resin specimens were measured using Dynamic Mechanical Analysis. With increasing aging time a corresponding increase in storage modulus was found. Increases in the storage modulus of the epoxy matrix subsequently resulted in a higher state of predicted stress within the matrix material from representative volume element analyses. Various parameters common to unidirectional composites were numerically investigated and found to have varying levels of impact on the prediction of the initiation of fatigue damage.     

Thermo-kinetic characteristics on stabilizing hetero-phase interface of metal matrix composites by crystal plasticity finite element method

Using dislocation-based constitutive modeling in three-dimension crystal plasticity finite element(3D CPFE)simulations,co-deformation and instability of hetero-phase interface in different material sys-tems were herein studied for polycrystalline metal matrix composites(MMCs).Local stress and strain fields in two types of 31ayer MMCs such as fcc/fcc Cu-Ag and fcc/bcc Cu-Nb have been predicted un-der simple compressive deformations.Accordingly,more severe strain-induced interface instability can be observed in the fcc/bcc systems than in the fcc/fcc systems upon refining to metallic nanolayered composites(MNCs).By detailed analysis of stress and strain localization,it has been demonstrated that the interface instability is always accompanied by high-stress concentration,i.e.,thermodynamic char-acteristics,or high strain prevention i.e.,kinetic characteristics,at the hetero-phase interface.It then follows that the thermodynamic driving force △G and the kinetic energy barrier Q during dislocation and shear banding can be adopted to classify the deformation modes,following the so-called thermo-kinetic correlation.Then by inserting a high density of high-energy interfaces into the Cu-Nb composites,such thermo-kinetic integration at the hetero-phase interface allows a successful establishment of MMCs with the high △G-high Q deformation mode,which ensures high hardening and uniform strain distri-bution,thus efficiently suppressing the shear band,stabilizing the hetero-phase interface,and obtaining an exceptional combination in strength and ductility.Such hetero-phase interface chosen by a couple of thermodynamics and kinetics can be defined as breaking the thermo-kinetic correlation and has been proposed for artificially designing MNCs.     

Stochastic nonlinear failure analysis of laminated composite plates under compressive transverse loading

This paper present the second ordered statistics of first-ply failure response of laminated composite plate with random material properties under random loading. The basic formulation is based on higher order shear deformation plate theory (HSDT) with the geometrically nonlinearity in the von-Karman. The direct iterative based C⁰ nonlinear finite element method combined with mean centered first order perturbation technique developed by the authors are extended and successfully applied nonlinearity for failure problem with a reasonable accuracy to predict the second order statistics (standard deviation) of first-ply failure response using Tsai-Wu and Hoffman failure criterion with macroscopic analysis. Typical numerical results for various combinations of boundary conditions, plate thickness ratios, aspect ratios, laminates scheme and layers, elastic modulus ratios have been presented to illustrate the application of developed procedure. Some new results are presented and examined which clearly demonstrated the importance of the randomness in the system parameters in the failure response of the structures subjected to transverse loadings.     

A combined elastoplastic damage model for progressive failure analysis of composite materials and structures

The paper is concerned with the development and verification of a combined elastoplastic damage model for the progressive failure analysis of composite materials and structures. The model accounts for the irreversible strains caused by plasticity effects and material properties degradation due to the damage initiation and development. The strain-driven implicit integration procedure is developed using equations of continuum damage mechanics, plasticity theory and includes the return mapping algorithm. A tangent operator consistent with the integration procedure is derived to ensure a computational efficiency of the Newton–Raphson method in the finite element analysis. The algorithm is implemented in Abaqus as a user-defined subroutine. The efficiency of the constitutive model and computational procedure is demonstrated using the analysis of the progressive failure of composite laminates containing through holes and subjected to in-plane uniaxial tensile loading. It has been shown that the predicted results agree well with the experimental data reported in the literature.     

Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model

Nonlinear free vibration behavior of laminated composite curved panel under hygrothermal environment is investigated in this article. The mathematical model of the laminated panel is developed using Green–Lagrange-type geometrical nonlinearity in the framework of higher-order mid-plane kinematics. The corrugated composite properties are evaluated through the micromechanical model and all the nonlinear higher-order terms are included in the present model for the sake of generality. The equation of vibrated panel is obtained using Hamilton's principle and discretized with the help of the finite element steps. The solutions are computed numerically using the direct iterative method. The effect of parameters on the nonlinear vibration responses is examined thoroughly by solving the wide variety of numerical examples.     

Simulation of the cabling process for Rutherford cables: An advanced finite element model

In all existing large particle accelerators (Tevatron, HERA, RHIC, LHC) the main superconducting magnets are based on Rutherford cables, which are characterized by having: strands fully transposed with respect to the magnetic field, a significant compaction that assures a large engineering critical current density and a geometry that allows efficient winding of the coils. The Nb₃Sn magnets developed in the framework of the HL-LHC project for improving the luminosity of the Large Hadron Collider (LHC) are also based on Rutherford cables. Due to the characteristics of Nb₃Sn wires, the cabling process has become a crucial step in the magnet manufacturing. During cabling the wires experience large plastic deformations that strongly modify the geometrical dimensions of the sub-elements constituting the superconducting strand. These deformations are particularly severe on the cable edges and can result in a significant reduction of the cable critical current as well as of the Residual Resistivity Ratio (RRR) of the stabilizing copper. In order to understand the main parameters that rule the cabling process and their impact on the cable performance, CERN has developed a 3D Finite Element (FE) model based on the LS-Dyna® software that simulates the whole cabling process. In the paper the model is presented together with a comparison between experimental and numerical results for a copper cable produced at CERN.     

Reliability predictions of laminated composite plates with random system parameters

Reliability predictions of laminated composite plates with random system parameters subjected to transverse loads are performed using different methods. System parameters such as material properties, layer thicknesses, and lamina strengths of a laminated composite plate are treated as base-line random variables and an appropriate failure criterion is used to construct the limit state equation of the plate in the reliability analysis. Based on the statistics of the base-line random variables obtained from experiments, different methods, namely, Monte Carlo method, β method, and first-order second moment method, are used to calculate the reliability of the laminated composite plates. In the first-order second moment method, the stochastic finite element method is used to derive for the statistics of the first-ply failure load of the laminated composite plates from those of the base-line random variables. The reliability of the laminated plate is then computed using the theoretically determined statistics together with an assumed probability distribution function of the first-ply failure load. The feasibility and accuracy of the different methods are studied by means of the experimental data of centrally loaded laminated composite plates with different lay-ups. The suitability of several commonly used failure criteria for reliability analysis of laminated composite plates is also investigated by means of several examples.