CLOSED-FORM SOLUTIONS FOR FORCES ON CONICAL-NOSED PENETRATORS INTO GEOLOGICAL TARGETS WITH CONSTANT SHEAR STRENGTH

Closed-form solutions of several elastic-plastic models which predict forces on conical-nosed penetrators into geological targets are developed. The constitutive description of the targets is guided by triaxial material test data for concrete and sea ice. These target materials are described by a linear hydrostat, a Tresca yield criterion with a tension cutoff and material density. The analyses are simplified by employing the cylindrical cavity expansion approximation, which idealizes the target as thin, independent layers normal to the penetration direction and simplifies the analyses to one-dimensional wave propagation in the radial direction. The governing equations are then reduced to nonlinear ordinary differential equations with a similarity transformation, linearized and solved in closed-form. These approximate linearized solutions are compared with exact results from nonlinear analyses, and excellent agreements are shown for a wide range of practical parameters. Finally, predictions from the theory are compared with the deceleration histories of several penetrators which were air-dropped into sea ice.