Constitutive equations for reliable projectile penetration analysis into a concrete medium

This article analyzes the fundamental question of the mechanical properties representation in penetration analysis and its effect on the calculated results. Penetration analysis into a concrete target with a specified uniaxial compressive strength was carried out using different material models appearing in software libraries. These models determine the specific material equation of state and shear strength envelope related to the concrete uniaxial compressive strength. Different results were obtained for the same concrete strength. This proves that the unconfined compressive strength is not the governing parameter which determines the projectile penetration characteristics and that a large variation of results is obtained from different models. Analysis was then carried out on a case with documented constitutive properties of a concrete target that was penetrated by an instrumented projectile. The predicted penetration depth and the projectile deceleration time history were compared with the measured data, and very good correspondence was obtained. This proved that the specific properties of the penetrated medium should be incorporated in the analysis to properly predict the penetration event. The study then examined the commonly used approximation of a linearized equation of state and a linear Mohr–Coulomb model, replacing the true non-linear equations of state and the true non-linear shear strength dependence, and the linearized relationships' effect on the analyzed results was assessed. A detailed study of the solution sensitivity to different parameters of the Mohr–Coulomb relationship then followed, and its effect on different penetration parameters (nose embedment duration, nose embedment velocity, penetration depth, peak deceleration, quasi-static deceleration) has been examined, to demonstrate how a perturbation in assumed concrete properties affects the solution of the penetration problem. The article illuminates the role of the constitutive equations on penetration analysis and the importance of the proper selection of the representative expressions and of their approximations.