Simulation of Buckling-Induced Failure in Composite Laminates

This contribution presents a simple model for the analysis of buckling–induced failure in thin–walled composite laminates in the framework of the finite element method. The plies are modeled with shear deformable geometrically non–linear four–node shell elements which are layered according to the classical laminate theory. Shear locking effects are reduced via the well–known assumed natural strains (ANS) approach. A ply discount model is applied for the successive failure of the plies. The cohesive zone approach which is implemented in so–called interface elements is employed for delamination. The failure processes are history dependent leading to non–recurring stiffness degradation in areas where damage is detected. A numerical example with experimental evidence highlights the performance and applicability of the proposed model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Predicting delamination in multilayered CFRP laminates accounting for different failure modes

Carbon fiber reinforced plastics (CFRP) are mostly used in multilayered laminates, which consist of several very thin layers stacked over each other. For such laminated structures, delamination represents one of the most critical states of failure. In order to predict both the onset as well as the propagation of delamination, a cohesive zone-like continuum damage model is proposed in this paper. This damage model is directly incorporated into a solid-shell finite element with finite thickness. Further, the formulation is capable of considering the interaction of different failure modes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Simple Model for the Simulation of Delamination in Fiber-ReinforcedComposite Laminates under Mixed-Mode Loading Conditions

For a reliable prediction of the mechanical behavior of unidirectional fiber-reinforced composite laminates (FRCL), it is inevitable to take into account various damage and fracture mechanisms. In this work, delamination under arbitrary mixedmode loading conditions is examined in the framework of the finite element method. Delamination is assumed to be caused by failure of the resin-rich area in the interface between two layers of FRCL's. In this work, a cohesive interface elementin terms of natural stress-strain relationships which allows to describe the interlaminar mechanical behavior of FRCL's is introduced. The proposed model prevents the restoration of cohesion in the interface. The interpenetration of the crack faces is avoided by incorporating a simple contact algorithm. A representative numerical example shows the applicability of the proposed concept. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A few typical delamination patterns of compressed thin films

In this paper we consider compressed flat thin films on rigid substrates. Residual compressive stresses arising e.g. from temperature loading are the driving quantities of the irreversible delamination process. A Reissner–Mindlin shell formulation is used as a model for the thin film, since small geometrical imperfections are considered to initiate buckling. For the interface we postulate the existence of a cohesive free energy as a function of the opening displacement vector and internal variables. The irreversible delamination process is described using a cohesive law of exponential type, where the parameters depend on the combination of the modes I, II and III. In order to analyse the delamination process exactly we use the energy criterion of the steady-state growth. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of shear bands in solids by means of computational homogenization

A novel fully three–dimensional framework for the numerical analysis of shear bands in solids undergoing large deformations is presented. The effect of micro shear bands on the macroscopic material response is computed by means of a homogenization strategy. More precisely, a strain–driven approach which complies well with displacement–driven finite element formulations is adopted. The proposed implementation is based on periodic boundary conditions for the micro–scale. Details about the implementation of the resulting constraints into a three–dimensional framework are discussed. The shear bands occurring at the micro–scale are modeled by a cohesive zone law, i.e., the tangential component of the traction vector governs the relative shear sliding displacement. This law is embedded into a Strong Discontinuity Approach (SDA). To account for realistic sliding modes, multiple shear bands are allowed to form and propagate in each finite element. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

层合板壳脱层曲面的有限元分析

通过建立一类新的参考面有限单元,得到适应于分析层合板壳脱层屈曲问题的有限元方法,指出了利用Ｍｉｎｄｌｉｎ假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元,这一方法确保了位移场的合理性和协调条件满足,为验证参考而单元的有效性和协调还对壳体脱层屈曲的几个算例作了数值分析。     

层合板壳脱层屈曲的有限元分析

通过建立一类新的参考面有限单元,得到适用于分析层合板壳脱层屈曲问题的有限元方法。指出了利用Mindlin假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元。这一方法确保了位移场的合理性和协调条件的满足。为验证参考面单元的有效性,还对壳体脱层屈曲的几个算例作了数值分析。     

A combined finite/discrete element algorithm for delamination analysis of composites

A combined finite/discrete element method is developed to model delamination behaviour in laminated composites. A penalty based algorithm is employed to evaluate the interlaminar stress state. The failure surface for delamination is defined by a Chang-Springer criterion, and the interlaminar crack propagation is achieved by a standard discrete element contact/release algorithm. The ability of the method for simulation of this behaviour is assessed by solving standard test cases available from the literature.     

Finite element construction for simulating delamination of sandwich composite plates and masses

Displacements and transverse normal stresses in sandwich plates and masses have been approximated by the Ambartsumyan iterative approach to constructing mathematical models of the stress-strain state of sandwich structures. A linear distribution of the displacements in the sandwich structure is set up as the first step of the iterative process, while in the subsequent steps the displacement approximations with higher-order polynomials are obtained. The approximation of the compression stresses is based on Hooke's law using the expression of the tangential displacements in the second step and the normal displacements in the third step of the iterative process. Two shear functions are introduced. The finite element is rectangular and has four nodes. The number of degrees of freedom of finite elements is independent of the quantity of the layers that may be orthotropic. The finite element allows us to simulate delamination by a thin low-modulus interlayer. In doing so, the quantity of the layers increases, while the order of the resolving set of equations does not grow. A number of numerical experiments were carried out. It has been shown that the delamination can greatly increase the level of the stresses in the structure. This effect is especially significant for thin structures. The stresses are somewhat lower when taking into account the interlaminar friction.Submitted to the 10th International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 251–263, March–April, 1998.     

Experimental and numerical investigation of paperboard creasing

Laminated paperboard is widely used in packaging products. It usually consists of multiple layers bonded to each other by starch or adhesion. The indentation of fold lines (creasing) plays a crucial role during the whole converting process. It is important to control delamination and other damage effects to arrive at commercial cartons with high quality. Thus, the aim of this study is to describe the material behavior of a laminated paperboard during the creasing process. The paperboard was considered as a laminate of three different layers, and each was modeled separately with an anisotropic elastic-plastic material model while a cohesive zone approach described the opening behavior in between. The initial yielding was given by the Hill's 48 yield criterion, while the isotropic strain hardening was described by a power law hardening function. To calibrate the material parameters, a sequence of tensile and compression tests was conducted for each layer in different directions to account for the material's anisotropy. Finally, the creasing process was investigated using a two-dimensional plane strain finite element model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Element Modelling of Cracks Based on the Partition of Unity Method

In this paper a finite element model for the analysis of brittle materials in the post cracking regime is presented. The model allows the representation of failure zones several times smaller than the structure itself using relatively coarse finite element meshes. The formulation is based on the partition of unity method. Discontinuous shape functions are used to enrich the continuous approximation of the displacement field where a crack has opened [2]. The magnitude of the displacement jump is determined by extra degrees of freedom at existing nodes. The crack path is completely independent of the structure of the mesh and is continuous across element boundaries. To model inelastic deformations around the crack tip a cohesive crack model is used. A representative numerical example illustrates the performance of the proposed model.     

An Adaptive Finite Element Approach for Brittle Fracture

The extension of the finite element method to take discrete fracture and failure modes into account is a current field of research. In recent times, first results in terms of cohesive element formulations have been introduced into commercial applications. Such element formulations are able to cover the discrete behaviour of interfaces between different materials or the mechanical processes of thin layers. These approaches are not suitable for simulations with unknown crack paths in homogeneous materials, due to the initial elastic phase of the material formulation and the necessity to define potential crack paths a priori. The presented strategy starts with an unextended model and modifies the structure during the computations in terms of an adaptive procedure. The idea is to generate additional elements, based on the cohesive element formulation, to approximate arbitrary crack paths. For this purpose, a failure criterion is introduced. For nodes where the limiting value is reached, cohesive elements are introduced between the volume element boundaries of accordingly facets and corresponding nodes are duplicated. Necessary modifications for this application on system level as well as the element and the material formulation are introduced. By means of some numerical examples, the functionality of the presented procedure is demonstrated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A generalized cohesive element technique for arbitrary crack motion

A computational method for arbitrary crack motion through a finite element mesh, termed as the generalized cohesive element technique, is presented. In this method, an element with an internal discontinuity is replaced by two superimposed elements with a combination of original and imaginary nodes. Conventional cohesive zone modeling, limited to crack propagation along the edges of the elements, is extended to incorporate the intra-element mixed-mode crack propagation. Proposed numerical technique has been shown to be quite accurate, robust and mesh insensitive provided the cohesive zone ahead of the crack tip is resolved adequately. A series of numerical examples is presented to demonstrate the validity and applicability of the proposed method.     

Analysis of the free-edge effect in composite laminates by the boundary finite element method

Because of the risk of delamination due to high interlaminar stresses in the vicinity of free edges of composite laminates, there is a strong interest in efficient methods for the analysis of this free-edge effect. By the example of a symmetric [0°/90°]_s cross-ply laminate, the Boundary Finite Element Method is presented as a very efficient numerical method, which combines the advantages of the finite element method and the boundary element method. Analogously to the boundary element method, only the boundary is discretized, while the element formulation is finite element based. The resultant stress field is shown to be in very good agreement qualitatively and quantitatively with the comparative finite element analysis. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 355–366, March–April, 2000.     

Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure

Thermoelastic deflection and corresponding stresses of the pre-damaged layered panel structure are investigated numerically in this article including the large deformation kinematics under the linearly varying temperature field. The composite structural deformation kinematics is derived using two different polynomial type of kinematic theories including the through-thickness stretching effect. The inter-laminar separation between the adjacent layers is incurred via the sub-laminate approach and Green–Lagrange strain to count the total structural deformation. Also, the intermittent displacement continuity conditions are imposed in the current mathematical model to establish the displacement continuity between the separated layers. The variational principle is adopted for the evaluation of the nonlinear structural equilibrium equations and solved via total Lagrangian approach. The convergence and the corresponding validity of the currently derived nonlinear finite element solutions are checked by solving different sets of numerical examples. Additionally, the comprehensive inferences are drawn from various numerical examples for the well-defined important input parameter including the size, position, and location of delamination.     

The role of transverse stretching in the delamination fracture of softcore sandwich plates

This paper presents the semi-layerwise analysis of structural sandwich plates with through-width delamination. The mechanical model of rectangular plates is based on the method of four equivalent single layers and the system of exact kinematic conditions. An important improvement compared to a previous formulation is the consideration of linear and quadratic stretching term in the transverse displacement component. Three different delamination scenarios are investigated: core-core failure, face-core delamination and the face-face failure. By applying the first- and second-order laminated plate theories and the principle of virtual work the governing equations are derived. The equilibrium equations are solved under Lévy type boundary conditions using the state-space approach. Solutions for the mechanical fields are provided and compared to 3D finite element results. The energy release rate distributions along the delamination front are also determined using the J-integral. Although the stress resultants by transverse stretching do not influence directly the J-integral, the results indicate that this effect improves the accuracy of the model in general, and substantially influences the results of the first-order plate theory in the case of the face-face delamination.     

Implementation of a cohesive zone model for the investigation of the dynamic behavior of a rotating shaft with a transverse crack

The influence of a transverse crack on the vibration of a rotating shaft has been at the focus of attention of many researchers. The knowledge of the dynamic behavior of cracked shaft has helped in predicting the presence of a crack in a rotor. Here, the changing stiffness of the cracked shaft is investigated based on a cohesive zone model. This model is developed for mode-I plane strain and accounts for triaxiality of the stress state explicitly by using basic elastic-plastic constitutive relations. Then, the proposed numerical solution is compared to the switching crack model, which is based on linear elastic fracture mechanics. The cohesive zone model is implemented in finite element techniques to predict and to analyse the dynamic behavior of cracked rotor system. Timoshenko beam theory is used to model the discrete shaft under the effect of gravity, unbalance force and gyroscopic effect. The analysis includes the cohesive function for describing the breathing crack and the reduction of the second moment of area of the element at the location of the crack. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of the Three-Dimensional Stress State in Composite Shell Structures with Mixed Finite Elements

Being able to compute the complete three-dimensional stress state in layered composite shell structures is essential in order to examine complicated interlaminar failure modes such as delamination. We lay out a mixed finite element formulation with independent displacements, rotations, stress resultants and shell strains. A mixed hybrid shell element with 4 nodes and 5 or 6 nodal degrees of freedom is developed, so that the element formulation can also be used for problems with shell intersections. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

含分层复合材料层合梁弯曲问题的一般解法

基于一阶剪切梁理论,考虑分层边缘区域的变形特点,提出了含穿透分层复合材料梁模型．与传统分层模型不同,该文将未分层部分看作上下子梁,放弃了传统模型中分层前缘横截面始终保持平面的假设．通过分层前缘的位移连续条件和内力连续条件,建立了粘合段和分层段的控制方程．并且,应用该模型对不同边界条件下含不同分层尺寸对称和非对称分层的复合材料层合梁弯曲问题进行了求解,结果与三维有限元计算的结果一致,从而证明了模型的有效性和适用性．     

Simulation of skin-stiffener debonding in stiffened carbon/epoxy panels

Aircraft fuselage structures are typically composed of a curved skin connected to longitudinal stiffeners. They are nowadays made of carbon/epoxy laminates. Skin-stiffener debonding can lead to a significant reduction of their compressive loadcarrying capacity in the postbuckling range of response. This work examines this effect in the framework of the finite element method. A zero-thickness interface element written in terms of cohesive tractions and relative displacements is derived which is inserted between skin and stiffener. A special cohesive law already presented in [1, 2] describes the softening behavior of the interface while taking into account contact conditions. A numerical example shows the applicability of the model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)