Similarity analysis of projectile penetration into concrete

A dimensionless model for the depth of penetration (DOP) of a projectile penetrating into a concrete target, based on the similarity theory involving intermediate asymptotics, complete similarity, and incomplete similarity is presented. The calculated numerical results are in good agreement with previous experimental data, including two sets of full-scale and twenty-four sets of sub-scale penetration of non-deformable projectiles into concrete targets. Moreover, compared with several empirical and semi-empirical DOP models, the new model is applicable within a relatively broader range, including the penetration of both sub-scale and full-scale projectiles. For the limitations of the validity, dimensionless parameters II₃ =ψt/ψ larger than 12, II₄ = (ψ³f)/(Mv₀²) smaller than 0.1, and the initial impact velocity of the projectile less than about 900 m/s to 1000 m/s are necessary for the model.