The impact torsional buckling for the rigid plastic cylindrical shell

By using the energy criterion in[3],the impact torsional buckling for the rigid plastic cylindrical shell is studied.The linear dynamic torsional buckling equations for the rigid plastic shell is drived,and the critical impact velocity is given.     

On the stress–strain states of cellular materials under high loading rates

A virtual Taylor impact of cellular materials is analyzed with a wave propagation technique, i.e. the Lagrangian analysis method, of which the main advantage is that no pre-assumed constitutive relationship is required. Time histories of particle velocity, local strain, and stress profiles are calculated to present the local stress–strain history curves, from which the dynamic stress–strain states are obtained.The present results reveal that the dynamic-rigid-plastic hardening(D-R-PH) material model introduced in a previous study of our group is in good agreement with the dynamic stress–strain states under high loading rates obtained by the Lagrangian analysis method. It directly reflects the effectiveness and feasibility of the D-R-PH material model for the cellular materials under high loading rates.     

Dynamic tensile characterization of pig skin

The strain-rate dependent response of porcine skin oriented in the fiber direction is explored under tensile loading. Quasi-static response was obtained at strain rates in the range of 10-3s-1to 25 s-1. Characterization of the response at even greater strain rates is accomplished by measuring the spatio-temporal evolution of the particle velocity and strain in a thin strip subjected to high speed impact loading that generates uniaxial stress conditions. These experiments indicate the formation of shock waves; the shock Hugoniot that relates particle velocity to the shock velocity and the dynamic stress to dynamic strain is obtained directly through experimental measurements, without any assumptions regarding the constitutive properties of the material.     

A Physical Model of the Structure and Attenuation of Shock Waves in Metals

In this paper,a physical model of the structure and attenuation of shockwaves in metals is presented.In order to establish the constitutive equa-tions of materials under high velocity deformation and to study the struc-ture of transition zone of shock wave.two independent approaches are in-volved.Firstly,the specific internal energy is decomposed into the elasticcompression energy and elastic deformation energy,and the later is represent-ed by an expansion to third-order terms in elastic strain and entropy.includ-ing the coupling effect of heat and mechanical energy.Secondly,a plasticrelaxation function describing the behaviour of plastic flow under high tem-perature and high pressure is suggested from the viewpoint of dislocationdynamics.In addition.a group of ordinary differential equations has beenbuilt to determine the thermo-mechanical state variables in the transitionzone of a steady shock wave and the thickness of the high pressure shockwave.and an analytical solution of the equations can be foun     

Modeling the mechanics of HMX detonation using a Taylor–Galerkin scheme

Design of energetic materials is an exciting area in mechanics and materials science. Energetic composite materials are used as propellants, explosives, and fuel cell components. Energy release in these materials are accompanied by extreme events: shock waves travel at typical speeds of several thousand meters per second and the peak pressures can reach hundreds of gigapascals. In this paper, we develop a reactive dynamics code for modeling detonation wave features in one such material. The key contribution in this paper is an integrated algorithm to incorporate equations of state, Arrhenius kinetics, and mixing rules for particle detonation in a Taylor–Galerkin finite element simulation. We show that the scheme captures the distinct features of detonation waves, and the detonation velocity compares well with experiments reported in literature.     

Thermal energy storage： Challenges and the role of particle technology

Thermal energy is at the heart of the whole energy chain providing a main linkage between the primary and secondary energy sources. Thermal energy storage （TES） has a pivotal role to play in the energy chain and hence in future low carbon economy. However, a competitive TES technology requires a number of scientific and technological challenges to be addressed including TES materials, TES components and devices, and integration of TES devices with energy networks and associated dynamic optimization. This paper provides a perspective of TES technology with a focus on TES materials challenges using molten salts based phase change materials for medium and high temperature applications. Two key challenges for the molten salt based TES materials are chemical incompatibility and low thermal conductivity. The use of composite materials provides an avenue to meeting the challenges. Such composite materials consist of a phase change material, a structural supporting material, and a thermal conductivity enhancement material. The properties of the supporting material could determine the dispersion of the thermal con- ductivity enhancement material in the salt. A right combination of the salt, the structural supporting material, and the thermal conductivity enhancement material could give a hierarchical structure that is able to encapsulate the molten salt and give a substantial enhancement in the thermal conductivity. Understanding of the structure-property relationships for the composite is essential for the formulation design and fabrication of the composite materials. Linking materials properties to the system level performance is recommended as a key future direction of research.     

On the behaviour characterization of metallic cellular materials under impact loading

This paper reviews the common mechanical features of the metallic cellular material under impact loading as well as the characterization methods of such behaviours. The main focus is on the innovations of various testing methods at impact loading rates.Following aspects were discussed in details.（1） The use of soft nylon Hopkinson/Kolsky bar for an enhanced measuring accuracy in order to assess if there is a strength enhancement or not for this class of cellular materials under moderate impact loading;（2） The use of digital image correlations to determine the strain fields during the tests to confirm the existence of a pseudo-shock wave propagation inside the cellular material under high speed impact： （3） The use of new combined shear compression device to determine the loading envelop of cellular materials under impact multiaxial loadings.     

Analytical models for the penetration of semi-infinite targets by rigid, deformable and erosive long rods

A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.     

Mechanical behaviors and damage constitutive model of ceramics under shock compression

One-stage light gas gun was utilized to study the dynamic mechanical properties of AD90 alumina subjected to the shock loading. Manganin gauges were adopted to obtain the stress-time histories. The velocity interferometer system for any reflector （VISAR） was used to obtain the free surface velocity profile and determine the Hugoniot elastic limit. The Hugoniot curves were fitted with the experimental data. From Hugoniot curves the compressive behaviors of AD90 alumina were found to change typically from elastic to ＂plastic＂. The dynamic mechanical behaviors for alumina under impact loadings were analyzed by using the path line principle of Lagrange analysis, including the nonlinear characteristics, the strain rate dependence, the dispersion and declination of shock wave in the material. A damage model applicable to ceramics subjected to dynamic compressive loading has been developed. The model was based on the damage micromechanics and wing crack nucleation and growth. The effects of parameters of both the micro-cracks nucleation and the initial crack size on the dynamic fracture strength were discussed. The results of the dynamic damage evolution model were compared with the experimental results and a good agreement was found.     

The Riemann problem for nonlinear degenerate wave equations

This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case.     

A NUMERICAL ANALYSIS OF THREE-DIMENSIONAL THERMOELASTIC STRESS WAVE PROPAGATION PROBLEM

This paper is concerned with the numerical technique based on the method of character-istics for three-dimensional dynamic thermoelastic problems. A numerical example for the three-di-mensional stress wave propagation in a thermoelastic bar of square cross section subjected to both animpact loading and a thermal shock is presented.     

AN ANALYTICAL SOLUTION OF G.I.TAYLOR’S THEORY OF PLASTIC DEFORMATION IN IMPACT OF CYLINDRICAL PROJECTILES AND ITS IMPROVEMENT

The theory of plastic deformation in the impact of cylindrical projec-tiles on rigid targets was first introduced by G.I.Taylor(1948).The importance of this theorg lies in the fact that the dgnamic yieldstrength of the materials can be determined from the measurement ofthe plastic deformation of flat-ended cylindrical projectiles.Fromthe experimental results.we find that the dynamic gield strengthis independent of impact velocity.and that it is higher than the sta-tic yield strength in general,and several times higher than the sta-tic yield strength in certain cases.This gives an important founda-tion for the studg of elastoplastic impact problems in qeneral.How-ever,it is well known that the complexity of differential equationsin Taylor’s theory compelled us to use the troublesome numerical so-lution.In this paper,the analgtical solution of all the equationsin Taylor’s theory is given in parametrical form and the results arediscussed in detail.In the latter part of this paper,the method of calculatio     

AN ANALYTICAL SOLUTION OF G. I. TAYLOR’S THEORY OF PLASTIC DEFORMATION IN IMPACT OF CYLINDRICAL PROJECTILES AND ITS IMPROVEMENT

The theory of plastic deformation in the impact of cylindrical projectiles on rigid targets was first introduced by G. I. Taylor(1948)^[1]. The importance of this theory lies in the fact that the dynamic yield strength of the materials can be determined from the measurement of the plastic deformation of flat-ended cylindrical projectiles. From the experimental results^[2] we find that the dynamic yield strength is independent of impact velocity, and that it is higher than the static yield strength in general, and several times higher than the static yield strength in certain cases. This gives an important foundation for the study of elastoplastic impact problems in general. However, it is well known that the complexity of differential equations in Taylor’s theory compelled us to use the troublesome numerical solution. In this paper, the analytical solution of all the equations in Taylor’s theory is given in parametrical form and the results are discussed in detail.In the latter part of this paper, the method of calculation of impulse of impact is improved by considering the processes of radial’ movement of materials. The analytical solution of the improved theory shows that it gives better agreement with the experimental results than that of original Taylor’s theory.     

Effect of the grain size on the macroscopic response of aluminum to shock loading

Shock tests of two lots of a 1420 aluminum-lithium alloy are performed. The mean grain size is 24 μm in the first lot and 1.6 μm in the second lot obtained by the method of equal-channel angular pressing. Two characteristics of dynamic strength of the material were determined in experiments on the high-velocity impact of flat samples: threshold of dynamic stability with respect to compression on the fore front of the compression pulse and spall strength of the material. The materials of both types have an identical threshold of dynamic stability with respect to compression, whereas the spall strength of the microcrystalline alloy is 20% greater than the spall strength of the polycrystalline alloy. The reason is the consumption of energy on structure formation in the coarse-grain material in passing to a larger-scale structural level (in the case with a fine-grain material, such a structure is available in the initial state). The experiments reveal the presence of a second plastic front whose amplitude is approximately 10% of the first plastic front. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 135–146, November–December, 2007.     

Mechanical response of encapsulated shear thickening fluid

In this investigation,the hard-to-handle shear thickening fluid (STF) is successfully encapsulated for easy handling and re-processing in the application of promising impact resistant material.Double-walled macroscopic STF capsules are synthesized using a convenientprocess by instilling the diluted STF droplets into reaction solution.The obtained STF capsules show significant shear thickening response to dynamic impact in comparison to quasistatic compression in terms of 154 times higher absorbed nominal strain energy.This innovative method opens a new window to design and manufacture versatile impact resistant materials and structures.     

Experimental and theoretical investigation of the failure behavior of a reinforced concrete target under high-energy penetration

The dynamic mechanical properties of concrete and reinforced concrete targets subjected to high-speed projectile impact loading have a significant influence on the impact resistance of protective structures.In this study,high-speed projectile penetration and perforation of concrete and reinforced concrete structures was carried out to determine the high-energy impact loading.The failure behaviors of projectile penetration and perforation of the concrete and reinforced concrete targets were investigated,and the destruction characteristics of the targets were measured.An analytical model was established using the principle of minimum potential energy.The results show that the theoretical predictions are consistent with the experimental data,indicating that the energy method is effective for predicting the dynamic mechanical properties of concrete and reinforced concrete targets under high-speed projectile penetration.     

Investigation on the plastic work-heat conversion coefficient of 7075-T651 aluminum alloy during an impact process based on infrared temperature measurement technology

The plastic work-heat conversion coefficient is one key parameter for studying the work-heat conversion under dynamic deformation of materials. To explore this coefficient of 7075-T651 aluminum alloy under dynamic compression, dynamic compression experiments using the Hopkinson bar under four groups of strain rates were conducted, and the temperature signals were measured by constructing a transient infrared temperature measurement system. According to stress versus strain data as well as the corresponding temperature data obtained through the experiments, the influences of the strain and the strain rate on the coefficient of plastic work converted to heat were analyzed.The experimental results show that the coefficient of plastic work converted to heat of 7075-T651 aluminum alloy is not a constant at the range of 0.85–1 and is closely related to the strain and the strain rate. The change of internal structure of material under high strain rate reduces its energy storage capacity, and makes almost all plastic work convert into heat.     

Jet formation in shock-heavy gas bubble interaction

The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF 6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF 6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analysis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pressure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.     

Nonlinear flexural waves and chaos behavior in finite-deflection Timoshenko beam

Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills, the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case, a shock wave solution is given. The small perturbations are further introduced, arising from the damping and the external load to an original Hamilton system, and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov＇s method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.     

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.