Sergey L. Lopatnikov

Dynamics of metal foam deformation during Taylor cylinder–Hopkinson bar impact experiment

Abstract Analytical solutions for dynamic deformation of foam materials during the Taylor cylinder–Hopkinson bar impact experiment were obtained. It was shown that shock wave of foam collapse appears during the fast impact. The results of this experiment can be used in estimating the average material properties of the foam under dynamic loading conditions. Results show that the un-deformed and change in length of foam specimens are in good agreement between theory and experiment, as well as numerical analysis.

High-velocity plate impact of metal foams

Abstract The ballistic impact of a massive, effectively 1-D plate on an initially stationary foam layer is considered. It is shown that four discrete velocity regimes must be considered. Two of these regimes are of major interest for ballistic impact studies. Regime 2 considers the case when the initial velocity of the plate is lower than the sound velocity of the constitutive material of the foam, but higher than the linear sound velocity of foam. Regime 3 considers the case when the initial plate velocity is lower than the linear sound velocity of the foam; but remains higher than the effective sound velocity for a perturbation in which the amplitude lies in the so-called “plateau region” of the static stress–strain diagram. Analytical solutions for dynamic deformation and energy absorption of foam materials under the plate impact condition for Regimes 2 and 3 are developed. It has been shown that in both cases, a compressive shock wave appears. The physical difference between these two regimes entails not only the creation of a shock front associated with the collapsing foam, but also an acoustic precursor in the case of Regime 3. As a result, the efficiency of energy absorption in Regime 2 depends only on the initial density of the foam, the density of the constitutive material of the foam, and the areal mass of the impacting plate, whereas the efficiency of energy absorption for Regime 3 also depends on the Mach number and the critical stress of the foam. Numerical plate impact simulations have been carried out in impact Regime 2. Explicit finite element analysis is performed using LS-DYNA 960. The time history of dynamic deformation and energy of the impact plate is presented. The numerical prediction is found to be in good agreement with the analytical results.

Poroelasticity-III: Conditions on the Interfaces

In this, the third part of our paper, we continue consideration of the major elements of the poroelastic theory which we started in Parts I and II (in Lopatnikov and Gillespie, Transp Porous Media, 84:471–492, 2010; Transp Porous Media, 89:475–486, 2011). This third part is devoted to considering the general interfacial conditions, consistent with the governing differential equations of the theory. Specifically, we will consider associated mass and momentum conservation laws. Because we developed the theory by construction, general boundary conditions obtained can be applied to the arbitrary interfaces: boundaries between different materials or, for example, moving interfaces of the shock fronts. We do not consider here the last group of conservation laws: the energy conservation laws, which we are going to introduce and investigate in the special part, devoted to the shock wave propagation. In the meantime, special attention is devoted to discussing the problem of “partial permeability” of the interfaces reflected in the literature. Particularly we show, that in the stationary case, the general theory allows only two conditions: either the interface is completely penetrable, or the interface is completely impenetrable. Thus, “partial permeability” solution always appears as only an approximation of an exact dynamic problem, which includes either thin low-permeable interfacial layer (with permeable boundaries), or a non-homogeneous boundary containing permeable and non-permeable patterns.

Implementing the Split‐Hopkinson Pressure Bar Technique for Shear Thickening Fluid Evaluation

The split‐Hopkinson pressure bar experimental technique has been implemented to evaluate the high rate squeeze flow behavior of a concentrated shear thickening fluid (STF). This paper focuses on recent efforts into interpreting the high stress/deformation rate results. A 3D graphical representation is presented and approaches to developing constitutive relationships capable of describing the transient behavior of the STF are discussed.

Simple analytical model for fiber tensile failure due to droplet impact

We present a simple model of the mechanics of the transverse impact of a water droplet of finite size on a free-standing fiber. There are two major differences between the transversal impact of a liquid droplet and the impact of a solid projectile. The first difference is that the segment of the fiber interacting with the droplet is not required to move with the speed of the droplet as in the case of an impact of a solid projectile. The second difference is related to the duration of interaction between the fiber and impactor. In the case of a solid projectile, interaction is complete when either the fiber fails or the projectile is defeated. However, failure in the case of the impact of a droplet is governed particularly by the time of interaction with the liquid droplet, which is governed by the flow around the accelerating fiber that may lead to fiber failure. The analytical model assumes a droplet diameter much larger than the diameter of the fiber and predicts the transverse forces acting on the fibe...

Split Hopkinson Pressure Bar Data Reduction Methodology for Linear Materials with Memory

Abstract The classic split-Hopkinson pressure bar (SHPB) data reduction methodology is revisited. A complete one-dimensional analysis of the SHPB system is presented for linear-elastic and viscoelastic specimens, for which the specimen and bar diameters are equal. In general, the assumptions inherent in the classic SHPB data reduction method are found to be inconsistent. However, the classic SHPB data reduction scheme is applicable in the case of acoustically soft materials. These analyses are extended to explain major issues in the general linear elastic case, including materials with regular and singular memory. Exact expressions for the average stress and strain in the specimen and Fourier transform of the memory kernel function in terms of experimental parameters in the quasi-static limit are formulated. Dynamic adjustments associated with elastic and viscous relaxation processes are also derived.

Dynamics of a rigid plate impacting a glass plate: A one dimensional analysis considering failure-wave propagation

Dynamics of a rigid plate impacting a glass plate is presented considering failure-wave and shock-wave propagations in the target material in addition to an elastic precursor. A generalized one dimensional theoretical failure-shock-elastic (FSE) model is developed and later simplified to study different impact scenarios on glass. While the nonlinear equations of the FSE model is solved numerically, an analytical solution is obtained for the failure-elastic submodel. In solving the failure-shock model for glass, a condition describing the jump in particle velocities at the failure front is proposed based on experimental observations. Time histories of the displacement, velocity, and resistance force of the rigid impact plate are presented.

Dynamic Progressive Collapse of Closed Cell Aluminum Foam

Progressive collapse behavior of closed cell aluminum foam under multiple-impact loading is presented. A direct impact Hopkinson pressure bar set up is developed to impact aluminum foam cylinders with a striker bar at a constant impact velocity. The total length of the specimen before and after impact is measured. The incident bar response is recorded, and average stress in the specimen is calculated. The incremental plastic strain and maximum strain rate is calculated from basic test parameters. It has been shown that by conducting direct impact experiments at variable impact velocities, it is possible to determine the dynamic behavior of closed cell metal foams at constant strain rates.