A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson＇s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

Severe plastic deformation of commercially pure aluminum using novel equal channel angular expansion extrusion with spherical cavity

Equal channel angular expansion extrusion with spherical cavity(ECAEE-SC)was introduced as a novel severe plastic deformation(SPD)technique,which is capable of imposing large plastic strain and intrinsic back-pressure on the processed billet.The plastic deformation behaviors of commercially pure aluminum during ECAEE-SC process were investigated using finite element analysis DEFORM-3D simulation software.The material flow,the load history,the distribution of effective strain and mean stress in the billet were analyzed in comparison with conventional equal channel angular extrusion(ECAE)process.In addition,single-pass ECAEE-SC was experimentally conducted on commercially pure aluminum at room temperature for validation,and the evolution of microstructure and microhardness of as-processed material was discussed.It was shown that during the process,the material is in the ideal hydrostatic stress state and the load requirement for ECAEE-SC is much more than that for ECAE.After a single-pass ECAEE-SC,an average strain of 3.51 was accumulated in the billet with homogeneous distribution.Moreover,the microstructure was significantly refined and composed of equiaxed ultrafine grains with sub-micron size.Considerable improvement in the average microhardness of aluminum was also found,which was homogenized and increased from HV 36.61 to HV 70.20,denoting 91.75%improvement compared with that of the as-cast billet.

Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.

INTERPOLATION OF HEAD-RELATED TRANSFER FUNCTIONS USING SPHERICAL FOURIER EXPANSION

A new interpolation algorithm for Head-Related Transfer Function （HRTF） is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition （SVD） is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.

Estimation of compaction grouting pressure in strain softening soils

A new method was proposed to predict the limited compaction grouting pressure for the soft soils. Theoretical basis of the method considered the conical shear failure above the grout bulb. Using the Mohr-Coulomb yield criterion as the initial yield function, the limited compaction grouting pressure was determined, according to the softening elastic-plastic model based on the conventional triaxial compression tests to simulate the strain softening soils. The small strain in the elastic zone and large stain in the plastic zone and the rational yield function for the strain softening phase stage, the analytical solutions to the compaction grouting pressure were presented. The results indicate reasonable agreement and show a good potential of the proposed method for rationally optimizing the design of compaction grouting operations.

Finite Spherical Cavity Expansion Method for Layering Effect

A decay function for the layering effect during the projectile penetrating into layered targets is constructed, which is obtained via the theoretical solution of a dynamically expanding layered spherical cavity with finite radius in the layered targets that are assumed to be incom- pressible Mohr-Coulomb materials. By multiplying the decay function with the semi-empirical forcing functions that account for all the constitutive behavior of the targets, the forcing functions for the layered targets are obtained. Then, the forcing functions are used to represent the targets and are applied on the projectile surface as the pressure boundary condition where the projectile is modeled by an explicit transient dynamic finite element code. This methodology is implemented into ABAQUS explicit solver via the user subroutine VDLOAD, which eliminates the need for discretizing the targets and the need for the complex contact algorithm. In order to verify the proposed layering effect model, depth-of-penetration experiments of the 37 mm hard core pro-jectile penetrating into three sets of fiber concrete and soil layered targets are conducted. The predicted depths of penetration show good agreement with the experimental data. Furthermore, the influence of layering effect on projectile trajectory during earth penetration is investigated. It is found that the layering effect should be taken into account if the final position and trajectory of the projectile are the main concern.

Resistance of grid steel-tube-confined concrete targets against projectile impact: Experimental investigation and analytical engineering model

Steel-tube-confined concrete(STCC) targets are provided with excellent anti-penetration performance over semi-infinite concrete(SIC) targets since the steel tube imposes passive restraint on the in-filled concrete during the penetration process. Grid STCC system with square steel tubes is a potential solution to protective structures. In this paper, experiments of 9-cell grid STCC targets penetrated by 12.7 mm Armor Piercing Projectile(APP) were performed. The influence of side length and thickness of steel tube,steel ratio and impact velocity on anti-penetration performance were taken into account. Additionally,single-cell square STCC targets were also designed and tested for comparison with the 9-cell grid STCC targets. Damage modes and parameters of the tested targets were measured and discussed. Moreover,the stiffness of radial confinement of grid STCC targets is achieved according to the elastic solution of infinite cylindrical shell in Winkler medium. Furthermore, the penetration resistance and depth of penetration(DOP) for grid STCC targets are obtained on the basis of the dynamic finite spherical cavityexpansion(FSCE) models including radial confinement effect. It is shown that the 9-cell grid STCC targets with optimal dimension match of thickness and side length of steel tube can reduce the DOP by about17 % and 23 % in comparison with the SIC targets and single-cell square STCC targets, respectively, due to both the confinement of square steel tube to concrete in the impacted cell and the additional confinement of the surrounding cells to the impacted cell;the penetration resistance and DOP of the grid and cellular STCC targets with similar steel ratio is close, and thus the grid STCC targets with simpler manufacturing process and excellent in-plane expandability are preferred in engineering practice;moreover, the predicted results of DOP model based on the FSCE models agree well with the tested results with the maximum disparity less than 12 % and the proposed model is more applicable to the grid and cellular STCC targets with high radial confinement.

REALIZATION OF PEETRE K-MODULUS ON THE SPHERE

The Peetre K-modulus and the generalized. Riesz summability operators on the sphere are introduced. The convergence and boundedness of the Riesz operators are discussed. The strong and weak equivalence relationships of the K-moduli and the Riesz operators are presented. The Riesz operators can serve as a realization of the corresponding K-modulus.

Prediction of solar activities:Sunspot numbers and solar magnetic synoptic maps

The evolution of solar magnetic fields is significant for understanding and predicting solar activities.And our knowledge of solar magnetic fields largely depends on the photospheric magnetic field.In this paper,based on the spherical harmonic expansion of the photospheric magnetic field observed by Wilcox Solar Observatory,we analyze the time series of spherical harmonic coefficients and predict Sunspot Number as well as synoptic maps for Solar Cycle 25.We find that solar maximum years have complex short-period disturbances,and the time series of coefficient g_(7)~0 is nearly in-phase with Sunspot Number,which may be related to solar meridional circulation.Utilizing Long Short-Term Memory networks(LSTM),our prediction suggests that the maximum of Solar Cycle 25 is likely to occur in June 2024 with an error of 8 months,the peak sunspot number may be 166.9±22.6,and the next solar minimum may occur around January 2031.By incorporating Empirical Mode Decomposition,we enhance our forecast of synoptic maps truncated to Order 5,validating their relative reliability.This prediction not only addresses a gap in forecasting the global distribution of the solar magnetic field but also holds potential reference value for forthcoming solar observation plans.

Dilepton from Passage of Jets Through Spherical Expanding QGP

We calculate the large mass dileptons production from the jet-dilepton conversion in spherical expanding quark-gluon plasma at Relativistic Heavy Ion Collider（RHIC） and Large Hadron Collider（LHC） energies.The jetdilepton production exceeds the thermal and Drell Yan dilepton production in the large mass region of 4.5 GeV

PREDICTION OF PROJECTILE PENETRATION AND PERFORATION BY FINITE CAVITY EXPANSION METHOD WITH THE FREE-SURFACE EFFECT

With a target treated as the incompressible Tresca and Mohr-Coulomb material, by assuming that cavity expansion produces plastic-elastic and plastic-cracked-elastic response region, the decay function for the free-surface effect is constructed for metal and geological tar- gets, respectively. The forcing function for oblique penetration and perforation is obtained by multiplying the forcing function derived on the basis of infinite target assumption with the de- cay function. Then the projectile is modeled with an explicit transient dynamic finite element code and the target is represented by the forcing function as the pressure boundary condition. This methodology eliminates discretizing the target as well as the need for a complex contact algorithm and is implemented in ABAQUS explicit solver via the user subroutine VDLOAD. It is found that the free-surface effect must be considered in terms of the projectile deformation, residual velocity, projectile trajectory, ricochet limits and critical reverse velocity. The numerical predictions are in good agreement with the available experimental data if the free-surface effect is taken into account.

A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONAL WAVE-VECTOR SPACE AND ITS DIFFUSION LIMIT

The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.