Gabi Ben-Dor

Ballistic Impact: Recent Advances in Analytical Modeling of Plate Penetration Dynamics–A Review

This review covers studies dealing with simplified analytical models for ballistic penetration of an impactor into different solid media, namely, metals, soil, concrete, and composites at high speeds, but not at hypervelocities. The overview covers mainly papers that were published in the last decade, but not analyzed in previous reviews on impact dynamics. Both mathematical models and their engineering applications are considered. The review covers 280 citations. DOI: 10.1115/1.2048626

A parametric study of Mach reflection in steady flows

The flow fields associated with Mach reflection wave configurations in steady flows are analysed, and an analytical model for predicting the wave configurations is proposed. It is found that provided the flow field is free of far-field downstream influences, the Mach stem heights are solely determined by the set-up geometry for given incoming-flow Mach numbers. The point at which the Mach stem height equals zero is exactly at the von Neumann transition. For some parameters, the flow becomes choked before the Mach stem height approaches zero. It is suggested that the existence of a Mach reflection not only depends on the strength and the orientation of the incident shock wave, as prevails in von Neumanns three-shock theory, but also on the set-up geometry to which the Mach reflection wave configuration is attached. The parameter domain, beyond which the flow gets choked and hence a Mach reflection cannot be established, is calculated.

Shock wave interaction with cellular materials

The equations governing the head-on collision of a planar shock wave with a cellular material and a numerical scheme for solving the set of the governing equations were outlined. In addition, the condition for the transmitted compression waves to transform into a shock wave, inside the cellular material was introduced. It was proved analytically that a cellular material cannot be used as a means of reducing the pressure load acting on the end-wall of the shock tube. In subsequent papers, the interaction of planar shock waves with specific cellular materials, e.g., foams and honeycombs will be described in detail.

On the ballistic resistance of multi-layered targets with air gaps

Abstract High velocity penetration of a 3-D rigid sharp impactor into a ductile layered target with air gaps between the plates is studied using the assumption about the localized projectile-target interaction. The special property of the penetration phenomenon for conical-nosed impactors is established, namely, that the ballistic performance of the target is independent on the air gap widths and on the sequence of the plates in the target. Similar results are also obtained for 3-D non-conical impactors on the basis of some class of models. These findings are in good agreement with available experimental results.

Head-on Collision of Normal Shock Waves with Rigid Porous Materials

The head-011 collision of a planar shock wave with a rigid porous material has been investigated experimentally. The study indicated that unlike the reflection from a flexible porous material, where the transmitted compression waves do not converge to a sharp shock wave, in the case of a rigid porous material the transmitted compression waves do converge to a sharp shock wave, which decays as it propagates along the porous material.

Evolution of the balance equations in saturated thermoelastic porous media following abrupt simultaneous changes in pressure and temperature

A mathematical model is developed for saturated flow of a Newtonian fluid in a thermoelastic, homogeneous, isotropic porous medium domain under nonisothermal conditions. The model contains mass, momentum and energy balance equations. Both the momentum and energy balance equations have been developed to include a Forchheimer term which represents the interaction at the solid-fluid interface at high Reynolds numbers. The evolution of these equations, following an abrupt change in both fluid pressure and temperature, is presented. Using a dimensional analysis, four evolution periods are distinguished. At the very first instant, pressure, effective stress, and matrix temperature are found to be disturbed with no attenuation. During this stage, the temporal rate of pressure change is linearly proportional to that of the fluid temperature. In the second time period, nonlinear waves are formed in terms of solid deformation, fluid density, and velocities of phases. The equation describing heat transfer becomes parabolic. During the third evolution stage, the inertial and the dissipative terms are of equal order of magnitude. However, during the fourth time period, the fluids inertial terms subside, reducing the fluids momentum balance equation to the form of Darcys law. During this period, we note that the body and surface forces on the solid phase are balanced, while mechanical work and heat conduction of the phases are reduced.

Experimental and Numerical Study of Shock Wave Interaction with Perforated Plates

The flow developed behind shock wave transmitted through a screen or a perforated plat is initially highly unsteady and nonuniform. It contains multiple shock reflections and interactions with vortices shed from the open spaces of the barrier The present paper studies experimentally and theoretically/numerically the flow and wave pattern resulted from the interaction of an incident shock wave with a few different types of barriers, all having the same porosity but different geometries

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.

Optimal 3D impactors penetrating into layered targets

Abstract Optimization of 3D sharp high speed impactors with given form of a longitudinal contour, length, and volume, penetrating into layered ductile targets, both for conical and thin non-conical strikers using approximate models is studied. It is found that the impactor with the minimum drag moving in a homogenous target with a constant velocity penetrates to the maximal depth into a semi-infinite target and has the minimal ballistic limit when it penetrates into a finite thickness target, regardless of the distribution of the material properties of the target along its depth, the number of the layers, etc. Using the analogy with the hypersonic flow over the flying projectiles it is predicted that the optimal impactor should have a star-shaped form of the cross section. If an impactor has a polygonal cross sections allowing the inscribed circles, the ballistic limit and maximum depth of penetration are independent not only of the properties of the target but also of the form of the polygon in the cross section and equal to the corresponding values for the inscribed body of revolution.

Displacement waves in saturated thermoelastic porous media. I. basic equations

A complete set of macroscopic equations, the solution of which describes fluid and solid stresses, displacements and temperatures, evolving from an excitation of a saturated porous medium domain in the form of an abrupt pressure and temperature changes applied at the domains boundary is presented. The fluid is a compressible Newtonian one and the solid is thermoelastic. Nonisothermal conditions prevail. The set of equations includes mass, momentum and energy balance equations, constitutive relations and definitions. A simple example indicates that the fluid and solid displacements are described by two coupled wave equations.