On dimensionless numbers for predicting large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile

The principal objective of this study is to develop two empirical equations based on new dimensionless numbers for predicting large ductile transverse deformation of monolithic and multi-layered square targets due to a normal impact of a rigid spherical projectile. In the first step, a complete set of dimensionless parameters is generated based on the Buckingham π-theorem for nondimensionalization of the governing equations of quadrangular plates subjected to dynamic loading. New dimensionless numbers are suggested based on the dimensionless governing equations of the plate where consider the effect of the geometry of structural member and projectile, material strength and density, impact velocity of the projectile, and strain rate sensitivity of materials. The dimensionless numbers are taken into account according to the input and output experimental data pairs. Lastly, nonlinear relationships between the ratios of maximum permanent deflection to target thickness and dimensionless numbers are established by using a novel mathematical approach, namely, singular value decomposition method. The outcomes of the empirical equations compare well with the experimental results on the single and layered targets made of either mild steel or aluminum alloy or a combination of them and illustrate good agreement with experiments for different impact velocities ranging from 42 to 158 m/s. Hence, it seems that the methodology of the present study can readily be employed to derive straightforward closed-form equations for complicated processes where several experimental input and output data pairs are existing.