Propagation Properties of Shock Waves in Polyurethane Foam based on Atomistic Simulations

Porous materials are widely used in the field of protection because of their excellent energy absorption characteristics.In this work,a series of polyurethane microscopic models are established and the effect of porosity on the shock waves is studied with classical molecular dynamics simulations.Firstly,shock Hugoniot relations for different porosities are obtained,which compare well with the experimental data.The pores collapse and form local stress wave,which results in the complex multi-wave structure of the shock wave.The microstructure analysis shows that the local stress increases and the local velocity decreases gradually during the process of pore collapse to complete compaction.Finally,it leads to stress relaxation and velocity homogenization.The shock stress peaks can be fitted with two exponential functions,and the amplitude of attenuation coefficient decreases with the increase of density.Besides,the pore collapse under shock or non-shock are discussed by the entropy increase rate of the system.The energy is dissipated mainly through the multiple interactions of the waves under shock.The energy is dissipated mainly by the friction between atoms under non-shock.

Experimental and numerical study on protective effect of RC blast wall against air shock wave

Prototype experiments were carried out on the explosion-proof performance of the RC blast wall.The mass of TNT detonated in the experiments is 5 kg and 20 kg respectively.The shock wave overpressure was tested in different regions.The above experiments were numerically simulated,and the simulated shock wave overpressure waveforms were compared with that tested and given by CONWEP program.The results show that the numerically simulated waveform is slightly different from the test waveform,but similar to CONWEP waveform.Through dimensional analysis and numerical simulation under different working conditions,the equation for the attenuation rate of the diffraction overpressure behind the blast wall was obtained.According to the corresponding standards,the degree of casualties and the damage degree of the brick concrete building at a certain distance behind the wall can be determined when parameters are set.The above results can provide a reference for the design and construction of the reinforced concrete blast wall.

Blast waveform tailoring using controlled venting in blast simulators and shock tubes

A critical challenge of any blast simulation facility is in producing the widest possible pressure-impulse range for matching against equivalent high-explosive events.Shock tubes and blast simulators are often constrained with the lack of effective ways to control blast wave profiles and as a result have a limited performance range.Some wave shaping techniques employed in some facilities are reviewed but often necessitate extensive geometric modifications,inadvertently cause flow anomalies,and/or are only applicable under very specific configurations.This paper investigates controlled venting as an expedient way for waveforms to be tuned without requiring extensive modifications to the driver or existing geometry and could be widely applied by existing and future blast simulation and shock tube facilities.The use of controlled venting is demonstrated experimentally using the Advanced Blast Simulator(shock tube)at the Australian National Facility of Physical Blast Simulation and via numerical flow simulations with Computational Fluid Dynamics.Controlled venting is determined as an effective method for mitigating the impact of re-reflected waves within the blast simulator.This control method also allows for the adjustment of parameters such as tuning the peak overpressure,the positive phase duration,and modifying the magnitude of the negative phase and the secondary shock of the blast waves.This paper is concluded with an illustration of the potential expanded performance range of the Australian blast simulation facility when controlled venting for blast waveform tailoring as presented in this paper is applied.

Research advances in enhanced coal seam gas extraction by controllable shock wave fracturing

With the continuous increase of mining in depth,the gas extraction faces the challenges of low permeability,great ground stress,high temperature and large gas pressure in coal seam.The controllable shock wave(CSW),as a new method for enhancing permeability of coal seam to improve gas extraction,features in the advantages of high efficiency,eco-friendly,and low cost.In order to better utilize the CSW into gas extraction in coal mine,the mechanism and feasibility of CSW enhanced extraction need to be studied.In this paper,the basic principles,the experimental tests,the mathematical models,and the on-site tests of CSW fracturing coal seams are reviewed,thereby its future research directions are provided.Based on the different media between electrodes,the CSW can be divided into three categories:hydraulic effect,wire explosion and excitation of energetic materials by detonating wire.During the process of propagation and attenuation of the high-energy shock wave in coal,the shock wave and bubble pulsation work together to produce an enhanced permeability effect on the coal seam.The stronger the strength of the CSW is,the more cracks created in the coal is,and the greater the length,width and area of the cracks being.The repeated shock on the coal seam is conducive to the formation of complex network fracture system as well as the reduction of coal seam strength,but excessive shock frequency will also damage the coal structure,resulting in the limited effect of the enhanced gas extraction.Under the influence of ground stress,the crack propagation in coal seam will be restrained.The difference of horizontal principal stress has a significant impact on the shape,propagation direction and connectivity of the CSW induced cracks.The permeability enhancement effect of CSW is affected by the breakage degree of coal seam.The shock wave is absorbed by the broken coal,which may hinder the propagation of CSW,resulting in a poor effect of permeability enhancement.When arranging two adjacent boreholes for CSW permeability enhancement test,the spacing of boreholes should not be too close,which may lead to negative pressure mutual pulling in the early stage of drainage.At present,the accurate method for effectively predicting the CSW permeability enhanced range should be further investigated.

Experimental investigation on weak shock wave mitigation characteristics of flexible polyurethane foam and polyurea

In recent years,explosion shock wave has been considered as a signature injury of the current military conflicts.Although strong shock wave is lethal to the human body,weak shock wave can cause many more lasting consequences.To investigate the protection ability and characteristics of flexible materials and structures under weak shock wave loading,the blast wave produced by TNT explosive is loaded on the polyurethane foam with the density of 200.0 kg/m3(F-200)and 400.0 kg/m3(F-400),polyurea with the density of 1100.0 kg/m^(3)(P-1100)and structures composed of the two materials,which are intended for individual protection.Experimental results indicate that the shock wave is attenuated to weak pressure disturbance after interacting with the flexible materials which are not damaged.The shock wave protective capability of single-layer materials is dependent on their thickness,density and microscopic characteristics.The overpressure,maximum pressure rise rate and impulse of transmitted wave decrease exponentially with increase in sample thickness.For the same thickness,F-400 provides better protective capability than F-200 while P-1100 shows the best protective capability among the three materials.In this study,as the materials are not destroyed,F-200 with a thickness more than10.0 mm,F-400 with a thickness more than 4.0 mm,and P-1100 with a thickness more than 1.0 mm can attenuate the overpressure amplitude more than 90.0%.Further,multi-layer flexible composites are designed.Different layer layouts of designed structures and layer thickness of the single-layer materials can affect the protective performance.Within the research range,the structure in which polyurea is placed on the impact side shows the optimal shock wave protective performance,and the thicknesses of polyurea and polyurethane foam are 1.0 mm and 4.0 mm respectively.The overpressure attenuation rate reached maximum value of 93.3%and impulse attenuation capacity of this structure are better than those of single-layer polyurea and polyurethane foam with higher areal density.

Numerical and experimental investigation into the evolution of the shock wave when a muzzle jet impacts a constrained moving body

The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.

Extracorporeal shock wave therapy in treating ischial non-union following Bernese periacetabular osteotomy:A case report

BACKGROUND Extracorporeal shock wave therapy(ESWT)is increasingly being recognized as an advantageous alternative for treating non-union due to its efficacy and minimal associated complications.Non-union following Bernese periacetabular osteotomy(PAO)is particularly challenging,with a reported 55%delayed union and 8%non-union.Herein,we highlight a unique case of ischial non-union post-PAO treated successfully with a structured ESWT regimen.CASE SUMMARY A 50-year-old patient,diagnosed with left ischial non-union following the PAO,underwent six cycles of ESWT treatment across ten months.Each cycle,spaced four weeks apart,consisted of five consecutive ESWT sessions without anesthesia.Regular X-ray follow-ups showed progressive disappearance of the fracture line and fracture union.The patient ultimately achieved a satisfactory asymptomatic recovery and bone union.CONCLUSION The results from this case suggest that this ESWT regimen can be a promising non-invasive treatment strategy for non-union following PAO.

Evaluation of the Effectiveness and Efficiency of Extracorporeal Shock Wave Combined with Rehabilitation Training in the Treatment of Muscle Articulation Chronic Pain

Objective: To analyze the effect of combined extracorporeal shock wave and rehabilitation training treatment in patients with muscle articulation chronic pain (MACP). Methods: Ninety-seven MACP patients admitted to our hospital from September 2021 to September 2023 were randomly selected and were divided into Group A (control group, 46 cases, rehabilitation training treatment) and Group B (observation group, 51 cases, extracorporeal shock wave with rehabilitation training treatment), and outcomes of the two groups were compared. Results: The treatment efficiency, post-treatment clinical indexes (upper and lower limb function scores, activities of daily living (ADL) scores, visual analog scale (VAS) scores), and short-form 36 (SF-36) scores of Group B were better than those of Group A (P < 0.05). Conclusion: Combined extracorporeal shock wave and rehabilitation training treatment for MACP patients improved their limb function, daily activities, quality of life, and reduced pain.

Research on the distribution characteristics of explosive shock waves at different altitudes

There are great differences in the distribution characteristics of shock waves produced by ammunition explosions at different altitudes.At present,there are many studies on plain explosion shock waves,but there are few studies on the distribution characteristics of plateau explosion shock waves,and there is still a lack of complete analysis and evaluation methods.This paper compares and analyzes shock wave overpressure data at different altitudes,obtains the attenuation effect of different altitudes on the shock wave propagation process and proposes a calculation formula for shock wave overpressure considering the effect of altitude.The data analysis results show that at the same TNT equivalent and the same distance from the measuring point,the shock wave overpressure at high altitude is lower than that at low altitude.With the increase in the explosion center distance of the measuring point,the peak attenuation rate of the shock wave overpressure at high altitudes is smaller than that at low altitudes,and the peak attenuation rate of the shock wave overpressure at high altitudes gradually intensifies with increasing proportional distance.The average error between the shock wave overpressure and measured shock wave overpressure in a high-altitude environment obtained by using the above calculation formula is 11.1389%.Therefore,this method can effectively predict explosion shock wave overpressure in plateau environments and provides an effective calculation method for practical engineering tests.

THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS

In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region.Under the generalized entropy conditions,we find that there are different shock wave structures for different parameters.To guarantee the uniqueness of the solutions,we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters.Finally,we construct the Riemann solutions in some solvable regions.

ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY

This paper is concerned with an ideal polytropic model of non-viscous and heatconductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions.Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

Study on Collision Process of Opposing Unsteady Supersonic Jets and Shock Waves

Double pulsed-laser-ablation is a promising method to prepare nanoparticle composites. The backward movement of the plume after the collision with counter-propagating shock wave has been observed in experiments. In the present study, collision dynamics of the oppositely injected Si and Ge jets into a He background gas was numerically calculated as a simulation for double pulsed-laser-ablation. The experimentally observed backward movement was reproduced. The effect of distance between two jet exits on the distance of backward movement of the jet, BL, after the collision with the counter-propagating shock front was calculated to discuss the collision dynamics and to optimize the target distance for the experiment. We found that BL does not decrease monotonically with increasing distance between two jet exits, but has a maximum value at a certain distance. This behavior is discussed by calculating the expansion dynamics of an individual jet. Shock wave grows with time at the initial stage of the jet expansion and then attenuates;the density just behind the shock front for individual jet has a maximum value at a certain time and position. BL has a maximum value when the densities just behind the shock fronts for the individual jets have maximum values. This result is important for designing the appropriate distance between the two jet exits, i.e., the distance between the targets of double pulsed-laser-ablation.

NUMERICAL INVESTIGATION OF TOROIDAL SHOCK WAVES FOCUSING USING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD

A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.

Experimental study on the size effect on the equation of state of concretes under shock loading

Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.

Direct imaging of shock wave splitting in diamond at Mbar pressure

Understanding the behavior of matter at extreme pressures of the order of a megabar(Mbar)is essential to gain insight into various physical phenomena at macroscales—the formation of planets,young stars,and the cores of super-Earths,and at microscales—damage to ceramic materials and high-pressure plastic transformation and phase transitions in solids.Under dynamic compression of solids up to Mbar pressures,even a solid with high strength exhibits plastic properties,causing the induced shock wave to split in two:an elastic precursor and a plastic shock wave.This phenomenon is described by theoretical models based on indirect measurements of material response.The advent of x-ray free-electron lasers(XFELs)has made it possible to use their ultrashort pulses for direct observations of the propagation of shock waves in solid materials by the method of phase-contrast radiography.However,there is still a lack of comprehensive data for verification of theoretical models of different solids.Here,we present the results of an experiment in which the evolution of the coupled elastic-plastic wave structure in diamond was directly observed and studied with submicrometer spatial resolution,using the unique capabilities of the x-ray free-electron laser(XFEL).The direct measurements allowed,for the first time,the fitting and validation of the 2D failure model for diamond in the range of several Mbar.Our experimental approach opens new possibilities for the direct verification and construction of equations of state of matter in the ultra-high-stress range,which are relevant to solving a variety of problems in high-energy-density physics.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Instrumented assisted soft tissue mobilization vs extracorporeal shock wave therapy in treatment of myofascial pain syndrome

BACKGROUND Active myofascial trigger points(TrPs)often occur in the upper region of the upper trapezius(UT)muscle.These TrPs can be a significant source of neck,shoulder,and upper back pain and headaches.These TrPs and their related pain and disability can adversely affect an individual’s everyday routine functioning,work-related productivity,and general quality of life.AIM To investigate the effects of instrument assisted soft tissue mobilization(IASTM)vs extracorporeal shock wave therapy(ESWT)on the TrPs of the UT muscle.METHODS A randomized,single-blind,comparative clinical study was conducted at the Medical Center of the Egyptian Railway Station in Cairo.Forty patients(28 females and 12 males),aged between 20-years-old and 40-years-old,with active myofascial TrPs in the UT muscle were randomly assigned to two equal groups(A and B).Group A received IASTM,while group B received ESWT.Each group was treated twice weekly for 2 weeks.Both groups received muscle energy technique for the UT muscle.Patients were evaluated twice(pre-and posttreatment)for pain intensity using the visual analogue scale and for pain pressure threshold(PPT)using a pressure algometer.RESULTS Comparing the pre-and post-treatment mean values for all variables for group A,there were significant differences in pain intensity for TrP1 and TrP2(P=0.0001)and PPT for TrP1(P=0.0002)and TrP2(P=0.0001).Also,for group B,there were significant differences between the pre-and post-treatment pain intensity for TrP1 and TrP2 and PPT for TrP1 and TrP2(P=0.0001).There were no significant differences between the two groups in the post-treatment mean values of pain intensity for TrP1(P=0.9)and TrP2(P=0.76)and PPT for TrP1(P=0.09)and for TrP2(P=0.91).CONCLUSION IASTM and ESWT are effective methods for improving pain and PPT in patients with UT muscle TrPs.There is no significant difference between either treatment method.

Investigation of Supersonic Shock Wave Loading on Thin Metallic Sheets

Shock tube experiments were carried out to investigate dynamic behavior of Ultra-high hardness(UHH)steel and Aluminium(Al) sheets of 0.8 mm thickness at 0.55, 0.9 and 1.18 MPa peak-over pressure.Experimental results showed that center point deflection increases with an increase in peak-over pressure for Al sheets. However, UHH steel sheets showed negligible deformation when loaded at low peak-over pressures and showed sudden brittle failure at high peak-over pressures. Similar results were obtained by quasi-static testing, UHH steel failed abruptly while Al showed ductile behavior. Results from literature indicate that to protect structures against shock loading it is necessary that they dissipate energy via plastic deformation. The Al sheets were shown to deform plastically both in quasi-static and shock loading. Thus, hardness along with ductility is required to dissipate supersonic shock waves.

Flame behavior, shock wave, and instantaneous thermal field generated by unconfined vapor-liquid propylene oxide/air cloud detonation

Energy output and heating effects are essential for vapor-liquid fuel/air cloud detonation in the fuel-air explosive(FAE) applications or explosion accidents. The purpose of this study is to examine the dynamic large-size flame behavior, shock wave propagation law, and instantaneous thermal field generated by unconfined vapor-liquid propylene oxide(PO)/air cloud detonation. Based on computational fluid dynamics(CFD) and combustion theory, a numerical simulation is used to study the detonation process of a PO/air cloud produced by a double-event fuel-air explosive(DEFAE) of 2.16 kg. The large-scale flame behavior is characterized. The flame initially spreads radially and laterally in a wing shape. Subsequently,the developed flame increases with a larger aspect ratio. Moreover, the propagation laws of shock waves at different heights are discussed. The peak pressure of 1.3 m height level with a stepwise decline is obviously different from that of the ground with an amplitude of reversed ’N’ shape. In the vast majority of the first 6.9 m, the destructive effect of the shock wave near the ground is greater than that of the shock wave at 1.3 m height. Furthermore, the dynamic instantaneous isothermal field is demonstrated.The scaling relationship of various isotherms in the instantaneous thermal field with the flame and initial cloud is summarized. The comprehensive numerical model used in this study can be applied to determine the overpressure and temperature distribution in the entire fuel/air cloud detonation field,providing guidance for assessing the extent of damage caused by DEFAE detonation.

Extracorporeal shock wave for plantar flexor spasticity in spinal cord injury:A case report and review of literature

BACKGROUND Approximately 65%-78%of patients with a spinal cord injury(SCI)develop any symptom of spasticity.The aim of this study was to investigate the tolerability and short-term effects of radial extracorporeal shock wave therapy(r ESWT)on plantar flexor spasticity in a patient with incomplete SCI.CASE SUMMARY An 18-year-old man with an incomplete SCI completed five sessions of r ESWT.The primary outcomes were the changes in ankle-passive range of motion(APROM)and passive resistive force to ankle dorsiflexion.The outcomes were assessed at baseline(T0),immediately after treatment(T1)and 1 wk after the end of treatment(T2).The A-PROM increased by 15 degrees at T1 and 25 degrees at T2 compared with T0.The passive resistive force to ankle dorsiflexion at low velocity decreased by 33%at T1 and 55%at T2 in the gastrocnemius muscle and by 41%at T1 and 39%at T2 in the soleus muscle compared with T0.At high velocity,it also decreased by 44%at T1 and 30%at T2 in the gastrocnemius muscle compared with T0.However,in the soleus muscle,the change was minor,with a decrease of 12%at T1 and increased by 39%at T2 compared with T0.CONCLUSION In this patient,the findings showed that r ESWT combined with conventional therapy was well-tolerated and could be effective in improving A-PROM and passive resistive force to ankle dorsiflexion in the short-term.Further randomized controlled clinical trials with longer period of follow-up are necessary to confirm the results obtained in patients with SCI.