INTRODUCTION Much effort has been devoted in recent years towards obtaining improved understanding of damage evolution in composites subjected to impact, as evidenced by numerous publications in the open literature. Laminated composites impacted at low velocity by blunt objects are susceptible to the development of matrix cracks, fiber cracks, and interply delaminations[1]. While much of this damage may not be readily visible at the surface, it is capable of substantially reducing the residual strength and stiffness of the laminate. The resultant damage induced stress redistribution can lead to the failure of the component. Therefore, it is essential to be able to predict the damage evolution that occurs during the impact event so that the impact resistance, residual strength, and serviceable life of the laminate can be predicted. While few papers have appeared which attempt to address the three dimensional problem of impact, noteworthy are those of Wu and Springer [2,3] and of Chang and coworkers [4,5]. In these works a three dimensional transient dynamic finite element analysis is presented for the study of impact. However, delamination is not modeled. To the knowledge of the author none of the delamination damage models found in the published literature accounts for the development of the process zone ahead of the delamination front and the resulting nonlinearity in the interfacial mechanical response. Recently, the author has developed together with coworkers a micromechanics model for predicting the evolution of matrix cracking [6-8], and this model has previously been shown to be accurate when compared to experiment for polymeric composite plates subjected to quasi-static monotonic loading [9-12]. The problem of predicting the evolution of delaminations is much more complicated than that of matrix cracking. We have compared model predictions favorably to experiment for a variety of two dimensional examples [13,14]. While the problem of a single delamination in an elastic medium has successfully been solved [15], the prediction of multiple propagation of planar delaminations has only recently been considered. However, utilizing a cohesive zone model [6-24], the author and coworkers have been able to predict the evolution of up to seven simultaneous delaminations in a two dimensional setting [25], and this has been compared favorably to experimental results. Furthermore, the author and coworkers have also been able to predict the progression of multiple modes of damage in a two dimensional setting, as shown in Fig. 1. In addition, the algorithm has been utilized to predict multiple damage modes in a three dimensional plate with a circular cutout [26]. These predictions are among the most complex attempts known to date for predicting damage progression in composites subjected to impact. SOLUTION METHODOLOGY The model is three dimensional and computational in nature, utilizing the finite element method, and this model is implemented to the code SADISTIC [27]. Crack growth is simulated via the cohesive zone model currently under development by the author and coworkers [20-25]. The cohesive zone model for predicting damage evolution in laminated composite plates is cast within a three dimensional continuum finite element algorithm capable of simulating the evolution of matrix, fiber, and delamination cracking in composite structures subjected to ballistic impact. Cracking on vastly differing length scales is accounted for by employing global-local techniques, with appropriate damage dependent homogenization techniques introduced to bridge the disparate scales.
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