Recent developments in the aircraft industry towards substantially improving fuel economy and extending flight range have accelerated interest in the use of advanced composites as primary structural materials. The airframes of next-generation airliners will have substantial parts made of light-weight composites. This means that the engineering demands on the performance of fiber-reinforced composites will become greater. There is therefore a need to better understand and predict the multiple complex failure mechanisms in composite structures, and to devise more reliable failure theories and damage progression models. There is a large body of literature on progressive damage analysis in composites, much of which employs damage mechanics and material stiffness degradation methods. This article reviews some of the more recent work in this area and describes the issues pertinent to application in composite structures. The authors' ongoing research efforts in modeling and prediction of progressive damage through the relatively novel element-failure method (EFM), which has been coded into a user-defined UEL code in Abaqus, are discussed. In particular, results for notched composite laminates and pin-loaded (PL) analyses are shown and compared to experimental data. Although EFM is the computational platform on which the damage is advanced in the structure, the results are dependent on the choice of the failure criterion. Various failure criteria are used throughout the cases discussed herein, from the more traditional Tsai—Wu (TW) criterion to the very recently proposed micromechanics-based failure (MMF) criterion. The EFM may also be used with cohesive elements, with the former intended for modeling in-plane damage progression, while the latter for delamination onset and propagation. This hybrid EFM-cohesive element approach is illustrated with an analysis of double-notched composite laminate. The computational models are relatively robust up to and including ultimate load, and enable the mapping of extensive damage patterns in composite structures. They represent a suite of computational tools that extend the capability to model damage and failure propagation beyond initial failure prediction.

Modeling progressive damage in composite materials and structures poses considerable challenges because damage is, in general, complex and involves multiple modes such as delamination, transverse cracking, fiber breakage, fiber pullout, etc. Clearly, damage in composites can be investigated at different length scales, ranging from the micromechanical to the macromechanical specimen and structural scales. In this article, a simple but novel finite-element-based method for modeling progressive damage in fiber-reinforced composites is presented. The element-failure method (EFM) is based on the simple idea that the nodal forces of an element of a damaged composite material can be modified to reflect the general state of damage and loading. This has an advantage over the usual material property degradation approaches, i.e., because the stiffness matrix of the element is not changed, computational convergence is theoretically guaranteed, resulting in a robust modeling tool. The EFM, when employed with suitable micromechanicsbased failure criteria, may be a practical method for mapping damage initiation and propagation in composite structures. In this article, we present a micromechanical analysis for a new failure criterion called the strain invariant failure theory and the application of the EFM in the modeling of open-hole tension specimens. The micromechanical analysis yields a set of amplification factors, which are used to establish a set of micromechanically enhanced strain invariants for the failure criterion. The effects of material properties and volume fraction on the amplification factors are discussed.KEY WORDS: progressive damage, multiscale damage, element-failure method, strain invariant failure theory, micromechanical amplification.

Using micromanufactured S-shaped gold strings suspended in free space by means of window-frames, we experimentally demonstrate an electromagnetic meta-material (EM(3)) in which the metallic structures are no longer embedded in matrices or deposited on substrates such that the response is solely determined by the geometrical parameters and the properties of the metal. Two carefully aligned and assembled window-frames form a bi-layer chip that exhibits 2D left-handed pass-bands corresponding to two different magnetic resonant loops in the range of 1.4 to 2.2 THz as characterized by Fourier transform interferometry and numerical simulation. Chips have a comparably large useful area of 56 mm(2). Our results are a step towards providing EM(3) that fulfill the common notions of a material.

Predicting and modeling progressive damage in fiber-reinforced composite structures up to and including final failure is a considerable challenge because damage in composite materials is extremely complex, involving multiple modes, such as delamination, transverse microcracking, fiber breakage, fiber pullout, etc. Indeed, damage in composites should be studied at different length scales, ranging from the micromechanical to the macromechanical specimen and structural scales. The challenge, however, is in finding theories and methodologies that will faithfully reflect the structural effects of damage progression without involving an inordinate amount of detail (and effort) in the model, so that designers and engineers will have practical tools. In this article, a novel finite element-based method for modeling progressive damage in fiber-reinforced composites is presented. The element-failure method (EFM) is based on the simple idea that the nodal forces of an element of a damaged composite material can be modified to reflect the general state of damage and loading. This has an advantage over the usual material property degradation approaches in that because the stiffness matrix of the element is not changed, computational convergence is guaranteed, resulting in a robust modeling method. When employed with a suitable micromechanics-based failure criterion, it may evolve into an engineering tool for mapping damage initiation and propagation in composite structures. Here, we have utilized the micromechanical information contained in a new strain invariant failure theory (SIFT) to guide the nodal force modification scheme to model progressive damage. As an application of the SIFT-EFM approach, we present a rational nodal force modification scheme for the modeling of progressive damage in quasi-isotropic composite laminates with open holes, subjected to remote tensile loads. The proposed nodal force modification scheme assumes loss of load-bearing capability in the direction transverse to the fibers for the case of local transverse microcracking, and assumes total loss of load-bearing capability when both transverse microcracking and fiber rupture occur. The study investigates the effect of stacking or layup sequence and shows that it is important to refine the model in the through-thickness dimension and includes nodal force modification for the out-of-plane component. It reinforces the view that damage propagation in composites is a complex three-dimensional event. When compared with experimental data, the predicted damage maps and final failure loads show correct trends and reasonable agreement.

Despite the fact that fiber-reinforced composite materials have been extensively used in aerospace, defense and marine structures for many years, the high stiffness and strength properties of these materials have not yet been fully exploited. In many instances, overly rigid adherence to conservative design rules based on ‘black aluminum’ (symmetric quasi-isotropic graphite-epoxy laminates) has eroded these advantages significantly. Efforts to better understand the failure mechanisms and develop efficient and robust computational tools will lend more confidence to designers and engineers to realize better weight savings and improve damage tolerance. The search for efficient computational tools for the modeling of progressive damage in composites should be coupled with sufficient fidelity to ensure that the mechanisms of the complex failure modes are accurately represented. In an effort towards this goal, the authors have proposed the element-failure method (EFM) using 3D solid finite elements, which has been successfully applied to failure analysis of composite laminates. The EFM has advantages over the traditional material property degradation method (MPDM) because the stiffness matrix of the element is not changed, thereby improving computational convergence and saving in computational efforts. In this article, a plate element-based EFM (PEFM) is presented for modeling progressive damage in fiber-reinforced composites. The implementation in plate elements further improves the efficiency of computation, when compared to analyses with 3D elements. In conjunction with several different failure theories, the plate EFM is applied to model progressive damage in quasi-isotropic composite laminates with open-holes, subjected to remote tensile loading. A mesh sensitivity study shows that the EFM results are relatively independent of mesh size effects. When compared with experimental data, the predicted ultimate strengths and damage patterns show good agreement.

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SUMMARYThis paper develops an enriched element-failure method for delamination analysis of composite structures. This method combines discontinuous enrichments in the extended finite element method and element-failure concepts in the element-failure method within the finite element framework. An improved discontinuous enrichment function is presented to effectively model the kinked discontinuities; and, based on fracture mechanics, a general near-tip enrichment function is also derived from the asymptotic displacement fields to represent the discontinuity and local stress intensification around the crack-tip. The delamination is treated as a crack problem that is represented by the discontinuous enrichment functions and then the enrichments are transformed to external nodal forces applied to nodes around the crack. The crack and its propagation are modeled by the 'failed elements' that are applied to the external nodal forces. Delamination and crack kinking problems can be solved simultaneously without remeshing the model or re-assembling the stiffness matrix with this method. Examples are used to demonstrate the application of the proposed method to delamination analysis. The validity of the proposed method is verified and the simulation results show that both interlaminar delamination and crack kinking (intralaminar crack) occur in the cross-ply laminated plate, which is observed in the experiment.

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