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This article investigates the feasibility of utilizing adaptive kinematics to reduce the computational effort of finite element modeling of progressive damage and global failure in fiber-reinforced composite laminates. In the present context, adaptive kinematics refers to the selective use of different types of macroscopic laminate models for different regions of the computational domain, based on the solution complexity within each region. Each of these macroscopic laminate models can be distinguished by the manner in which the displacement field is assumed to vary through the thickness of the laminate. In the present study, kinematic adaptivity is made possible through the use of variable kinematic finite elements (VKFE) that are developed by hierarchically combining two or more types of assumed displacement fields in a single finite element domain. The hierarchical data structure of the VKFE greatly simplifies the process of connecting elements that represent different types of laminate theories, thus facilitating adaptive analysis. The adaptive kinematic concept is demonstrated for the bending of simply supported laminates that exhibit diffuse, widespread damage and laminate tensile test specimens that exhibit very intense localized damage due to the free edge effect. The results obtained in this study clearly demonstrate that the use of adaptive kinematics can significantly reduce the overall computational effort of progressive damage solutions without compromising solution accuracy.

This article examines the distribution of strain energy in the various component materials of actuated plates and investigates the manner in which the strain energy distribution is influenced by the actuated span-to-thickness ratio and the thickness of the adhesive bond layer. Furthermore, the article investigates the effect of modeling choices (e.g., kinematic assumptions and mesh density) on the predicted magnitude and mode of the dominant strain energy form in each component material. These computed parameters can be used to quantify the overall efficiency of an actuated plate in addition to aiding the understanding of the local mechanics that govern the process. The focus problem consists of a square aluminum plate with a single symmetric pair of surface-mounted piezoceramic actuators that are used to produce in-plane extension or bending in the aluminum plate. The behavior of the actuated plate is examined over a range of plate thicknesses and adhesive bond layer thicknesses by using a series of finite element models that feature different levels of kinematic complexity and different levels of two-dimensional (2-D) mesh density. The results of the study emphasize the need for discrete layer kinematics in determining the magnitude and mode of the dominant strain energy form in each constituent material; however, these computed parameters are shown to be rather insensitive to changes in 2-D mesh density. Most importantly, the study confirms the existence and quantifies the magnitude of the local kinematic effect, whereby a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and transverse normal deformation, thus reducing the amount of actuation energy available to produce in-plane deformation in the structural substrate.

This article discusses finite element modeling of progressive damage in the adhesive bond layers of actuated plates and investigates the reduction in actuation capacity caused by the damaged bond layers. The primary challenge posed by this class of problems stems from the vast range of geometric scales that are represented, with the thickness of the adhesive layer representing the smallest scale, the overall thickness of the actuated plate representing the intermediate scale, and the in-plane dimensions of the plate representing the largest scale. In multiscale problems, the overall efficiency of the numerical methodology is of paramount importance, thus model development is guided by the need to obtain a sufficiently accurate solution at an acceptable computational expense. In this study, this goal is achieved through the use of a hierarchical, displacement-based, 2-D finite element model that includes the first-order shear deformation (FSD) model, Type I layerwise models (LW1) and Type II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C0 continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C0 continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the individual material ply or, in the case of layerwise models, by the individual numerical layer. The results clearly demonstrate that the resulting model can efficiently simulate progressive damage in the adhesive layers. For rectangular actuator patches, the adhesive damage is highest near the corners of the actuator and is driven primarily by local concentrations in the transverse normal and transverse shear stresses. In contrast to previous studies that have shown that the inclusion of discrete layer transverse normal stress does not significantly influence the predicted global deformations, the present study shows that the transverse normal stress has a very significant effect in the initiation and progression of localized damage in the adhesive layers.

For the simple case of a homogeneous, isotropic plate with a single, symmetric pair of actuators, previous work by the authors has demonstrated the importance of including discrete layer kinematics in predicting the global response of the actuated plate. The inclusion of discrete layer kinematics permits accurate modeling of the so-called local kinematic effect, whereby a portion of the total actuation is diverted to the production of localized transverse shear deformation near the edges of the actuator, thus reducing the amount of actuation energy available to produce the desired global deformation mode. The present study expands upon this previous effort, investigating the magnitude of the local kinematic effect for more complex actuated plates involving fiber-reinforced laminated composite substrates with multiple symmetric pairs of actuators. The results obtained from finite element simulations using a wide range of kinematic assumptions conclusively demonstrate that as the actuated span-to-thickness ratio decreases, the models with discrete layer kinematics predict a smaller global response than the models that use equivalent-single-layer kinematics. Thus, the local kinematic effect is observed to influence the global response of the actuated plates regardless of the material constitution of the structural substrate and regardless of the in-plane spacing between actuator pairs.

The effects of accurately accounting for transverse shear strain, transverse normal strain, and discrete layer kinematics on the computed global response of actuated plates are investigated using a hierarchical displacement-based, two-dimensional (2-D) finite element model that is developed specifically for composite laminates. The hierarchical model is used to obtain the first-order shear deformation model, a higher-order cubic equivalent-singlelayer model, a type-I layerwise model, and a type-II layerwise model as special cases. Each of the first three models uses a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the models differ significantly in their assumed distribution of transverse shear strain. The type-II layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects. The scope of the study is restricted to homogeneous plates with surface-mounted actuators covering a wide range of span-to-thickness ratios. The results clearly demonstrate that as the span-to-thickness ratio of the actuated region decreases, discrete layer kinematics become very important for accurately characterizing the global response of the actuated plate. The set of laminate kinematic assumptions utilized by a particular model influence the predicted global response primarily through the so-called local kinematic effect where a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and localized transverse normal deformation in the vicinity of the actuator edges, thereby reducing the amount of actuation energy that is available for producing the intended global deformation mode.

In this article an efficient 3-D continuum damage mechanics formulation for composite laminates and its implementation into a finite element model that is based on the first order shear deformation theory of laminates are described. In the damage formulation each composite ply is treated as a homogeneous orthotropic material that can exhibit orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. This type of damage is efficiently described by a symmetric second order tensor field that serves as an evolving internal variable within the framework of irreversible thermodynamics. The damage tensor is continuous within each material ply of a given element, but can be discontinuous across material layer boundaries and inter-element boundaries. The resulting finite element formulation is shown to be robust, stable and efficient for the simulation of progressive damage and global failures in large-scale composite laminate problems. Numerical ex...

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C 0 continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C 0 continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.

A review of equivalent–single–layer and layerwise laminated plate theories and their finite element models is presented. The layerwise theory advanced by the senior author is presented and a variable displacement finite element model and mesh superposition techniques are described. A simultaneous multiple model approach that is based on the variable kinematic theory and the mesh superposition method are also described. The objective of the simultaneous multiple model approach is to match the most appropriate mathematical model with each subregion based on the physical characteristics, applied loading, expected behavior, and level of solution accuracy desired in that subregion. Thus solution economy is maximized without sacrificing the solution accuracy.

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

This chapter provides an overview of issues that are important in finite element modeling of progressive damage and failure in fiber-reinforced composite laminates. Topics discussed include the multiscale nature of composite laminate problems, equivalent single layer and layerwise laminate theories and models, macroscopic failure theories, computational homogenization and localization, and the application of continuum damage mechanics to composite laminate problems, with emphasis on methods that are practical for large scale analysis of composite structural components. Keywords: finite elements; composite laminates; damage; failure

A finite element modeling methodology is developed for the hierarchical, global/local analysis of laminated composite plates. The method incorporates a new variable kinematics, displacement-based, finite element that is developed using a multiple assumed displacement field approach. The variable kinematic elements provide a great degree of flexibility in defining the transverse (through thickness) variation of the assumed displacement field. The resulting finite element model permits different subregions of the computational domain to be described by different mathematical models. Enforcing displacement continuity along subregion boundaries requires only the specification of certain homogeneous essential boundary conditions, thus avoiding the inconvenience of multi-point constraints, penalty function methods, or special transition elements.

The layer—wise laminate theory of Reddy [1] is used to study interlaminar stress fields and carry out progressive failure analysis of composite laminates. The layer-wise theory not only predicts accurate interlaminar stress fields but it also provides a convenient format for modeling multiple delaminations. The computational model based on the layer—wise theory is capable of modeling free edge effects and energy release rates with the same accuracy as a conventional 3-D finite element model. The progressive failure analysis is based on an algorithm in which the damage is accounted through phenomenalogical failure criteria and a stiffness reduction coefficient. The stiffness reduction coefficient is used to define the equivalent material properties, which are used to update the stiffness matrix. It is demonstrated through an example problem that three-dimensional stress analysis is a necessary requirement but not sufficient to predict the failure behavior of composites laminate accurately.