Numerical analysis of projectile impact and deep penetration into earth media
Wagner, Mark H.; Kreyenhagen, Kenneth N.; Georke, W. S.
Contract ReportAbstract: A study was carried out to examine the utility, and some of the limitations, of using a finite-difference Lagrangian code to analyze relatively deep penetrations of projectiles into earth media. Numerical solutions were obtained for the normal impact of an 8-in. dia, 602-lb steel ogival projectile at 2000 fps into a soil/shale layered target. Two types of analyses were performed. In the first, the soil response, penetration dynamics, and projectile response were analyzed as one problem. The projectile was treated as an elastic-plastic, or deformable body, in order to determine the internal stress response. This computation was carried out for just the initial phase of penetration, until the nose was fully embedded in the soil. Problems were encountered with large numerical oscillations in the forces applied to the projectile (due to the strongly hysteretic soil model and to severe distortion of computational cells in the target). These problems can be overcome, but this type of calculation would still be cumbersome and time-consuming, due to the markedly different nature of the projectile response (primarily small, elastic strains) and of the soil response (severe plastic flow). A more practical approach is to separately analyze the penetration dynamics and the projectile response. This can be done by first calculating the penetration of the projectile treated as a non-deforming (rigid) body, thus determining the histories of projectile acceleration, velocity, and depth, as well as the spatial and temporal distribution of forces acting on the body. These force distributions can then be used as boundary conditions in a separate analysis of the internal stress dynamics of the projectile. In the second analysis, the projectile was treated as a rigid body, and its penetration to a depth of 22 ft was calculated. The average deceleration was 390 g's in the soil and 440 g's in the shale. The final velocity was 1984 fps. This is a more efficient approach, but it will still be very time-consuming to calculate an entire penetration event in this manner. Fortunately, because of the quasi steady state nature of penetration processes within a nominally homogeneous geologic layer, it is not necessary to calculate the entire penetration. The penetration dynamics and critical force loading conditions on the projectile can be determined with reasonable accuracy by analyzing just the initial embedment and those periods where the projectile is entering different geologic layers.
Soils and Pavements Laboratory (U.S.)Engineer Research and Development Center (U.S.)
Penetration; Projectiles; Terradynamics; Finite-difference codes; Soil mechanics; Numerical analysis; Mathematical analysis
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