Improved Florence model and optimization of two-component armor against single impact or two impacts G. Ben-Dor, A. Dubinsky, T. Elperin * Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel Available online 20 February 2008 Abstract A new version of the Florence model taking into account the ballistic resistance of the ceramic plate in a two-component armor is suggested, verified and used for armor optimization. The direct problems (maximization of the ballistic limit velocity for a given areal density (AD) or a total thickness (TT) of the armor) and the inverse problems (minimizations of AD or TT for a given impact velocity) are investigated in the case of a single impact. We also formulated and studied the armor optimization problems with a repeated impact. Numerical results are presented for aluminum/alumina armor. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Impact; Penetration; Two-component armor; Ceramics; Optimization 1. Introduction Two-component composite armors consisting of a cera- mic front plate and a ductile back plate attract considerable interest because of their high ballistic performance and light weight. Although numerous analytical models have been suggested for analyzing perforation of two-component cera- mic shields [1–11], Florence model [12] was found to be the most suitable for solving problems associated with armor optimization. Some early numerical results obtained with this approach have been presented in [12,13]. In the second study, the original model was slightly reworked and this modified version was later used for armor optimization against normal impact. Hetherington [14] investigated analytically the problem of determining the structure of the two-component armor with a given areal density (AD) that provides the maximum ballistic limit velocity (BLV). He suggested an approximate expression for the optimum value of the ratio of the front plate width to the back plate width. Wang and Lu [15] investigated a similar problem where the total thickness (TT) of the armor rather than the areal density (AD) was a given. Ben-Dor et al. [16–18] investigated problems of determining the armor with the maximum BLV for a given AD and the armor with the min- imum AD for a given impact velocity. In these studies, using appropriate dimensionless variables, the solutions of the optimization problems for an arbitrary two-component composite armor have been determined in an analytical form. Shi and Grow [19] investigated the problem of two- component armor optimal whereby both, the TT and the AD, are used as the constraints. Fawaz et al. [20] studied the problems in a generalized formulation when the armour materials are employed as the unknown design parameters. Some data relating to the comparison of the results of the armor optimization based on the Florence model with numerical simulations and experiments can be found in [21–23]. Studies [24,25] investigated a modified Florence’s model for the case of an oblique impact. In Florence model, the impactor was modeled as a short cylindrical rod that strikes the ceramic plate (Fig. 1). The ceramic plate breaks progressively into a cone of fractured material. The impact energy is transferred to the back plate which is deformed like a uniform membrane. 0263-8223/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2008.02.015 * Corresponding author. E-mail address: elperin@bgu.ac.il (T. Elperin). www.elsevier.com/locate/compstruct Available online at www.sciencedirect.com Composite Structures 88 (2009) 158–165