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This chapter provides an overview of the delamination growth in composite materials, cohesive interface models and finite element techniques used to simulate the interface elements. For completeness, the development and implementation of a new constitutive formula that stabilize the simulations and overcome numerical instabilities will be discussed in this chapter. Delamination is a mode of failure of laminated composite materials when subjected to transverse loads. It can cause a significant reduction in the compressive load-carrying capacity of a structure. Cohesive elements are widely used, in both forms of continuous interface elements and point cohesive elements, (Cui & Wisnom, 1993; De Moura et al., 1997; Reddy et al., 1997; Petrossian & Wisnom, 1998; Shahwan & Waas, 1997; Chen et al., 1999; Camanho et al., 2001) at the interface between solid finite elements to predict and to understand the damage behaviour in the interfaces of different layers in composite laminates. Many models have been introduced including: perfectly plastic, linear softening, progressive softening, and regressive softening (Camanho & Davila, 2004). Several ratedependent models have also been introduced (Glennie, 1971; Xu et al., 1991; Tvergaard & Hutchinson, 1996; Costanzo & Walton, 1997; Kubair et al., 2003). A rate-dependent cohesive zone model was first introduced by Glennie (Glennie, 1971), where the traction in the cohesive zone is a function of the crack opening displacement time derivative. Xu et al. (Xu et al., 1991) extended this model by adding a linearly decaying damage law. In each model the viscosity parameter (η ) is used to vary the degree of rate dependence. Kubair et al. (Kubair et al., 2003) thoroughly summarized the evolution of these rate-dependant models and provided the solution to the mode III steady-state crack growth problem as well as spontaneous propagation conditions. A main advantage of the use of cohesive elements is the capability to predict both onset and propagation of delamination without previous knowledge of the crack location and propagation direction. However, when using cohesive elements to simulate interface damage propagations, such as delamination propagation, there are two main problems. The first one is the numerical instability problem as pointed out by Mi et al. (Mi et al., 1998), Goncalves et al. (Goncalves et al., 2000), Gao and Bower (Gao & Bower, 2004) and Hu et al.

Finite Element Analysis of Delamination Growth in Composite Materials using LS-DYNA: Formulation and Implementation of New Cohesive Elements