A coupled DISC - 1D variational-difference approach to simulate the rigid projectile penetration into a concrete medium

A new effective approach to analyze penetration of a rigid projectile into a concrete medium is presented. The penetration analysis is based on the previously developed DISCS model approach in which the concrete medium is subdivided into discs, responding in the radial direction under plain strain conditions. The major new feature of this paper lies in the developed approach, which is a hybrid of the above DISCS model approach and of the 1D solution of cylindrical elastic-plastic wave propagation through the concrete medium in the radial direction. The 1D cylindrical problem in each of the discs planes is solved by the variational-difference method. The present approach uncouples the two-dimensional penetration problem into two connected one-dimensional problems and enables fast calculations of the projectile motion time history (i.e. deceleration, velocity and depth) as well as the displacement, velocity, strain and stress fields in the discs. The present approach is significantly faster and much simpler compared to a common 2-D axisymmetric analysis in which calculations in both radial and vertical directions are simultaneously performed and this requires much more computational time. An added efficiency is provided by the DISCS approach, which allows to perform analysis only in discs that are in contact with the projectile nose. This reduces considerably the volume of calculations, yet considers all discs that contribute to the instantaneous resistance and enables precise analysis of the penetration problem. The advanced modeling of a typical disc response yields a realistic acceleration time history that is very similar to test measured signals. Comparisons of the present approach analysis results with projectile decelerations and penetration depths as well as with available measured in-target radial stress time histories demonstrate the high fidelity of the proposed approach. The present approach predictions are in considerably closer agreement with test data compared with other simplified methods as well as with 2-D computational analysis results.