On the penetration of nonaxisymmetric bodies into a deformable solid medium and their shape optimization

We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].     

Optimal 3D impactors penetrating into layered targets

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.     

不同重力场下颗粒冲击过程的离散元分析

开展不同重力场下颗粒材料冲击动力学研究有助于加深对颗粒运动机制的理解和深空探测任务的实施。本文采用离散元模拟对颗粒介质受球形冲击物的冲击过程进行了数值模拟,并与地球重力下冲击的试验结果进行对比验证。在此基础上,进一步研究了重力加速度对冲击物动力学的影响规律。计算结果表明,在所有重力加速度下,冲击物的穿透深度d与冲击速度v₀的关系可以用Poncelet模型表达;d与冲击物下落的总高度H表现为d～Hⁿ的幂律关系,当H<10 m时,d与H的幂率标度为0.322,而H>10 m时,d与H的幂率标度下降到0.211。此外,穿透深度小于冲击物半径时,重力加速度对冲击物减速过程无影响。在所有的重力加速度下,当冲击速度大于5 m/s时,冲击物的持续碰撞时间t_c是恒定的,且与重力的-1/2次方呈正比。     

Investigation of the effect of nozzle shape on supersonic/hypersonic impactors designed for size discrimination of nanoparticles

In this study the flow field and the nanoparticle collection efficiency of supersonic/hypersonic impactors with different nozzle shapes were studied using a computational modeling approach.The aim of this study was to develop a nozzle design for supersonic/hypersonic impactors with the smallest possible cut-off size d_(50) and rather sharp collection efficiency curves.The simulation results show that the changes in the angle and width of a converging nozzle do not alter the cut-off size of the impactor;however,using a conical Laval nozzle with an L/D_n ratio less than or equal to 2 reduced d_(50).The effect of using a cap as a focuser in the nozzle of a supersonic/hypersonic impactor was also investigated.The results show that adding a cap in front of the nozzle had a noticeable effect on decreasing the cut-off size of the impactor.Both flat disks and conical caps were examined,and it was observed that the nozzle with the conical cap had a lower cut-off size.     

Penetration of a copper rod into a sandy target

This paper presents the results of experimental and theoretical studies of high-velocity penetration of cylindrical copper rods into sand. The hydrodynamic Alekseevskii-Tate theory is modified to determine the penetration depth and wear velocity of the material of the rod penetrating into soil target in the plastic and hydrodynamic stages of penetration. The case where the target material is significantly less strong than the rod (impactor) material is considered.     

On the penetration of a rotating impactor into an elastic-plastic medium

This research is devoted to the modeling of high-speed rectilinear penetration of a rigid axisymmetric body (impactor with a flat bluntness) into an elastic–plastic media with account for its rotation about the axis of symmetry. The body has an arbitrary shape of the meridian. The resistance to the motion is represented as the sum of the body drag and the contribution of friction. The dynamic system governing the body motion is derived and the qualitative and numerical analysis of the projectile movement and perforation of a slab are performed. The problem of shape optimization of impactor with a flat bluntness is studied using evolutionary algorithm.     

Experimental‐theoretical analysis of nonstationary interaction of deformable impactors with soil

An experimental method for determining the force of resistance to penetration of a deformable impactor into soft soil was developed in the inverted formulation: the impactor and the target exchange roles and the necessary parameters of contact interaction are recorded in an immovable measuring rod (impactor). To verify the basic principles of this experimental technique, wave processes were analyzed numerically using a modified Godunov's scheme. The applicability of various models of soil deformation was studied, and the calculation results obtained were compared with experimental data.     

Method of calculating the resistance force upon an impact on a composite target

A kinematically possible velocity field allowing calculation of all the necessary integrals in quadratures and obtaining an analytical solution for the resistance force induced by impactor penetration into the target is constructed. The Saint-Venant model of a rigid-plastic body and the theorem on the upper bound of the limit load are used in solving the problem. The essence of the method applied is using the equilibrium equation in the form of the Lagrange equation. The kinematically possible velocity field allows obtaining an upper bound of the limit load, i.e., estimating the resistance force to impactor penetration.     

Investigation of the effect of nozzle shape on supersonic/hypersonic impactors designed for size discrimination of nanoparticles

In this study the flow field and the nanoparticle collection efficiency of supersonic/hypersonic impactors with different nozzle shapes were studied using a computational modeling approach. The aim of this study was to develop a nozzle design for supersonic/hypersonic impactors with the smallest possible cut-off size d₅₀ and rather sharp collection efficiency curves. The simulation results show that the changes in the angle and width of a converging nozzle do not alter the cut-off size of the impactor; however, using a conical Laval nozzle with an L/D_n ratio less than or equal to 2 reduced d₅₀. The effect of using a cap as a focuser in the nozzle of a supersonic/hypersonic impactor was also investigated. The results show that adding a cap in front of the nozzle had a noticeable effect on decreasing the cut-off size of the impactor. Both flat disks and conical caps were examined, and it was observed that the nozzle with the conical cap had a lower cut-off size.     

On the stress state of shells penetrating into a deformable solid

The motion of an axisymmetric shell in a deformable solid medium is considered. It is assumed that the medium resistance is described by a two-term expression containing a constant term (the rigidity characteristic) and an inertial term quadratic with respect to the penetration velocity. A model of the impactor penetration with the normal interactions with the resisting medium taken into account is proposed. The membrane forces and the arising stresses are determined for decelerated motions of the impactor.     

A model of high speed penetration into ductile targets

A model developed by Mileiko et al. [J. Appl. Mech. Tech. Phys. 5 (1981) 711–713; Theor. Appl. Fracture Mech. 21 (1994) 9–16] describing a high speed penetration of an impactor into a ductile target is generalized.     

Experimental and numerical studies of impact on filament-wound composite cylinder

This study focused on the impact behavior of carbon-fiber-wrapped composite cylinders subjected to impact from flat-ended,hemispherical-nosed and conical-nosed impactors.Damage morphologies of the cylinders and mechanisms of the damage were analyzed.Change laws of the maximum impact forces,durations of impact processes and energies absorbed by the cylinders after impact with different impactors and impact energies were obtained.A finite element model was developed and the simulation results were in reasonable agreement with the tests.Finally,taking the flat-ended impactor as an example,stress distributions of the cylinders under pressurization and impact were discussed.     

Effect of air gaps on ballistic resistance of targets for conical impactors

High velocity penetration of a rigid conical impactor into a ductile target with air gaps between the plates is studied using the cylindrical cavity expansion approximation describing impactor–target interaction. It is showed that the latter model predicts improvement of the ballistic performance of the target with the increase of air gaps. It is found analytically that the ballistic limit velocity of the target consisting of N plates with a fixed total thickness with large air gaps increases with the increase of N. The conditions are discussed when the predicted effects can be most pronounced.     

Possibility of generating strong magnetic fields in conducting materials by the action of high-velocity penetrators

The possibility of increasing the intensity of a magnetic field produced previously in a conducting medium moving under the action of a high-velocity penetrating body is analyzed. A simplified model of the interaction of an impactor and a conducting target with a transverse magnetic field is constructed within the framework of a one-dimensional scheme. It is shown that the degree of increase in the field intensity is determined by the relation between the magnetic-field compressibility and diffusion factors, and the corresponding dimensionless determining parameters is determined. Magnetic-field compression is estimated for a perfectly conducting medium and media with real conductivity. The significance of the thermal and mechanical effects accompanying the penetration of an impactor into a target with a transverse magnetic field is assessed. Bauman Moscow State Technical University, Moscow 107005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 13–18, May–June, 2000.     

Modified Zener Theory to Accurately Predict Impact Force Histories for Soft Impactors Employing Spiral Sensing

While predicting the impact force histories from the Zener impact model with different material properties of impactors, several discrepancies were observed and reported in this article. To overcome these discrepancies, a modified Zener model is proposed to accurately calculate impact force histories. In the original Zener theory, nonlinear Hertzian contact law was used, and it was assumed that impact forces are transmitted through natural intensity factors depending on coupled physical properties of the plate and the impactor. However, when the force histories were predicted, a diverging trend appeared for softer materials with elastic moduli below 20 GPa. It is hypothesized that the primary reasons for this divergence are due to the contact time delay and the viscoelastic dissipation of energy, which are not considered in current Zener models. Several modifications of the model have been proposed since its inception, but it has been found that they are not independently sufficient to accurately predict impact force histories. In this article, a modified Zener theory is proposed introducing two new parameters in the governing differential equation derived from the sensor phase lag index and the dominant frequency band through a set of experiments employing a spiral sensing mechanism followed by an optimization process. The spiral lag index shows an unexpected peculiar trend with soft impactors (< 20 GPa), which are distinctly different from hard impactors and are judicially incorporated in the model. Furthermore, the force histories are accurately reconstructed with the proposed modifications.     

Generation of a magnetic field in the shear deformation region of a conducting material upon high–velocity penetration

It is shown that when a high–velocity impactor penetrates into a conducting target with a transverse magnetic field, conditions for considerable field amplification are produced in the shear deformation region on the lateral surface of the impactor. Field generation in a conducting medium deformed in shear is considered within the framework of a plane one–dimensional problem of magnetohydrodynamics. The results obtained indicate that along the boundary of the cavity produced by the impactor in the target with a magnetic field, a thin layer with a very high field intensity (about 100 T) is formed. The possibility of explosion of this layer due to the magnetic pressure acting in it is analyzed.     

Shape optimization of penetrator nose

A simplified procedure is suggested to optimize a penetrator's nose shape using localized impactor–target interaction model in the cases of penetration into a semi-infinite target and into a target with a finite thickness. Such a procedure establishes the similarity between the projectile's shape optimization in penetration dynamics and in aerodynamics of high speeds. The optimization of the impactor's nose shape can thus be reduced to the variational problem considered previously in connection with the projectile's shape optimization in high speed gas dynamics. Two examples from the literature are analyzed when impactor's shape optimization involved difficulties whereas the mathematically similar problem was solved before in aeromechanics. Some aspects of applying gas dynamics similarity for optimization of the impactor's shape for bodies of revolution are discussed.     

Localized interaction models with non-constant friction for rigid penetrating impactors

We suggest approximate penetration models for rigid body penetration that take into account sliding velocity (SV) and pressure dependence of the friction coefficient (FC). It is showed that introducing variable FC in a localized interaction model (LIM) yields a model that belongs to the class of LIM. We developed a general method for determining the depth of penetration (DOP) using the piecewise linear approximation of the impactor’s generatrix. For some classes of SV dependent friction models we obtained analytical formulas for calculating the DOP. Using the experimental data available in the literature, we determined the dependencies of FC vs. pressure and SV. We conducted numerical modeling of penetration of a metal striker into metal and concrete shields employing models with variable and constant FC. Numerical simulations showed that taking into account variable FC strongly effects the DOP when FC changes appreciably for large velocities that are characteristic for the high-speed penetration.     

卵形头部刚性弹侵彻厚靶的半解析模型

基于确定靶体中速度势和速度场的方法分析刚性卵形头部弹体对有限厚靶的侵彻问题。推导了靶体中速度场与应力场的计算方法,利用据此编制的计算程序,计算了卵形头部钢弹体对铝靶的侵彻与穿透问题,给出了侵彻深度与剩余速度同初始碰撞速度的关系。结果表明,在对实验参数不经过任何调整的情况下,得到了同试验曲线相吻合的结果。可以看出该方法的有效性。     

有限厚块石砌体钢筋混凝土结构板抗贯穿性能的实验研究

用花岗岩和混凝土制备出了花岗岩板、钢丝网混凝土板、花岗岩与钢丝网混凝土组合板、花岗岩块石砌体钢筋混凝土结构板4种类型的有限厚靶板。采用口径为30 mm的火炮作为发射装置,利用形状相同、材料强度不同的2种弹体对上述靶板进行了侵彻贯穿实验,比较了各类靶板抗侵彻贯穿破坏现象。结果表明,设计良好的块石砌体钢筋混凝土结构板具有优良的抗贯穿性能,且其抗贯穿性能与块石粒径、块石强度、块石砌筑方式、粘结强度和钢筋混凝土结构形式密切相关。