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For the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in-plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one-dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in-plane matrix cracks combined with the extend FEM. Figure 1. Typical matrix cracks and delaminations pattern resulted from low impact [12].delamination by macro-scopic damage initiation criteria, such as Choi-Wu [6,7] and Hashin criteria [22,23]. The cumulative effect of delamination can be described by the material degradation models at failure material point. The implementation of the damage mechanics methods is very simple. Because the damage is incorporated within the constitutive model, the damage mechanics methods are easily adapted to numerical approaches such as the FEM. But the real extension process of delamination can not be observed in the damage mechanics methods. In the fracture mechanics methods, linear elastic fracture mechanics (LEFM) is commonly applied for the problem of delamination. Although the fracture mechanics predictions for metallic materials has been widely adopted because of its relative simplicity and accuracy, it is not true for the delamination problem of composite laminates. LEFM is only suited to bonded composite where a realistic de-bonded defect can be defined and the loads produce a uniform linear strain regime. The cohesive fracture model addresses some of the limitations of LEFM, such as the material softening at the crack front and the damage initiation of the delamination in monolithic composites. For the fracture mechanics, the sensitivity to mesh shape still exists and will limit the applicability to the impact problems when used in conjunction with current nonadaptive FE methods. The primary advantage of the fracture mechanics methods is that fracture mechanics concepts can be readily incorporated, such as critical energy release rate. However, the adaptation of the fracture mechanics methods to FEA is somewhat more complicated, because it...

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