Perfect elastic-viscoplastic field at mode I dynamic propagating crack-tip

The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode Ⅰ crack according to each parameter. It is shown that stress and strain both possess exponential singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode I crack. It approaches the limiting case, crack-tip is under ultra-viscose situation and energy accumulates, crack-tip begins to propagate under different compression situations.

Dynamic analysis of major public health emergency transmission considering the dual-layer coupling of community–resident complex networks

We construct a dual-layer coupled complex network of communities and residents to represent the interconnected risk transmission network between communities and the disease transmission network among residents. It characterizes the process of infectious disease transmission among residents between communities through the SE2IHR model considering two types of infectors. By depicting a more fine-grained social structure and combining further simulation experiments, the study validates the crucial role of various prevention and control measures implemented by communities as primary executors in controlling the epidemic. Research shows that the geographical boundaries of communities and the social interaction patterns of residents have a significant impact on the spread of the epidemic, where early detection, isolation and treatment strategies at community level are essential for controlling the spread of the epidemic. In addition, the study explores the collaborative governance model and institutional advantages of communities and residents in epidemic prevention and control.

ASYMPTOTIC DYNAMIC SOLUTION TO THE MODE Ⅰ PROPAGATING CRACK-TIP FIELD IN ELASTIC-VISCOPLASTIC MATERIAL

A new elastic_viscoplastic mode was proposed to analyze the stress and strain fields surrounding the tip of a propagating mode Ⅰ cracks. A proper displacement pattern was suggested and asymptotic equations were derived, and numerical solutions were illustrated. The analysis and calculation show that the crack_tip field is of logarithmic singularity for smaller viscosity, however no solution exists for large viscosity. By a careful analysis and comparison, it is found that the present results retain all merits of those given by Gao Yu_chen, while removing existing problems.

Field structure at mode Ⅲ dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.

ELASTIC-VISCOPLASTIC FIELDS NEAR THE TIP OF A PROPAGATING CRACK UNDER ANTI-PLANE SHEAR

The elastic-viscoplastic model proposed by Bingham was used to analyse the stress and strain surrounding the tip of a propagating crack under antiplane shear.The proper displacement pattern was given;the asymptotic equations were derived and solved numerically.The analysis and calculation show that for smaller viscosity the crack-tip possesses logarthmic singularity,and for larger viscosity it possesses power-law singularity.In critical case,the two kinds of singularity are consistent with each other.The result revealed the important role of viscosity for crack-tip field.

Asymptotic analysis of mode Ⅰ propagating crack-tip field in a creeping material

Adopting an elastic-viscoplastic, the asymptotic problem of mode I propagat ing crack-tip field is investigated. Various asymptotic solutions resulting from the analysis of crack growing programs are presented. The analysis results show that the quasi-statically growing crack solutions are the special case of the dynamic propagating solutions. Therefore these two asymptotic solutions can be unified.

THE ASYMPTOTIC SOLUTION TO THE ANTIPLANE SHEAR DYNAMICCRACK-TIP FIELD IN AN ELASTIC STRAIN-SOFTENING VISCOPLASTIC MATERIAL

The elastic strain softening-viscoplastic model is given in this paper. Using this model, the asymptotic stress and strain equations surrounding the tip of a propagating crock are given and numerical results ale obtained under antiplane shear. The analysis and calculation show that at the crack tip the strain possesses logarithmic singularity (ln(R/r))(1/(n+1)) while the stress is like (ln(R/r))(-n/(n+1)), therefore the asymptotic behaviour of the elastic strain-softening viscoplastic field is revealed under the antiplane shear.

A Spatial-Temporal Network Perspective for the Propagation Dynamics of Air Traffic Delays

Intractable delays occur in air traffic due to the imbalance between ever-increasing air traffic demand and limited airspace capacity.As air traffic is associated with complex air transport systems,delays can be magnified and propagated throughout these systems,resulting in the emergent behavior known as delay propagation.An understanding of delay propagation dynamics is pertinent to modern air traffic management.In this work,we present a complex network perspective of delay propagation dynamics.Specifically,we model air traffic scenarios using spatial–temporal networks with airports as the nodes.To establish the dynamic edges between the nodes,we develop a delay propagation method and apply it to a given set of air traffic schedules.Based on the constructed spatial-temporal networks,we suggest three metrics-magnitude,severity,and speed-to gauge delay propagation dynamics.To validate the effectiveness of the proposed method,we carry out case studies on domestic flights in the Southeastern Asia region(SAR)and the United States.Experiments demonstrate that the propagation magnitude in terms of the number of flights affected by delay propagation and the amount of propagated delays for the US traffic are respectively five and ten times those of the SAR.Experiments further reveal that the propagation speed for US traffic is eight times faster than that of the SAR.The delay propagation dynamics reveal that about six hub airports in the SAR have significant propagated delays,while the situation in the United States is considerably worse,with a corresponding number of around 16.This work provides a potent tool for tracing the evolution of air traffic delays.

VISCOPLASTIC SOLUTION TO FIELD AT STEADILY PROPAGATING CRACK TIP IN LINEARHARDENING MATERIALS

An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tip-field of moving crack in linear-hardening materials under plane strain condition. Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain, it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power law exponent of the rate of effective plastic strain. Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of mode II dynamic propagating crack, which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient. The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials. The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero, and further approaches to the HR （Hui-Riedel） solution when the hardening coefficient is equal to zero.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Molecular dynamics study of thermal stress and heat propagation in tungsten under thermal shock

Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermo-elastic stress wave, corresponding to the collective displacement of atoms, is analyzed with the Lagrangian atomic stress method, of which the reliability is also analyzed. The stress wave velocity corresponds to the speed of sound in the material, which is not dependent on the thermal shock energy. The peak pressure of a normal stress wave increases with the increase of thermal shock energy. We analyze the temperature evolution of the thermal shock region according to the Fourier transformation. It can be seen that the “obvious” velocity of heat propagation is less than the velocity of the stress wave; further, that the thermo-elastic stress wave may contribute little to the transport of kinetic energy. The heat propagation can be described properly by the heat conduction equation. These results may be useful for understanding the process of the thermal shock of tungsten.

AN INVESTIGATION ON ASYMPTOTIC NEAR-TIP FIELDS OF DYNAMIC CRACK IN AN ELASTIC-PERFECTLY PLASTIC COMPRESSIBLE MATERIAL

The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of infinitesimal displacement gradient theory, the material is characterized by the Von Mises yield criterion and the associated J(2) flow theory of plasticity. Through rigorous mathematical analysis, this paper eliminates the possibilities of elastic unloading and continuous asymptotic fields with singular deformation, and then constructs a fully continuous and bounded asymptotic stress and strain field. It is found that in this solution there exists a parameter phi(0) which cannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly the variations of continuous stresses, velocities and strains around the crack tip are given numerically for different values of phi(0).

Dynamic propagation problems concerning surfaces of asymmetrical mode III crack subjected to moving loads

With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.

The propagation dynamics and stability of an intense laser beam in a radial power-law plasma channel

By containing ponderomotive self-channeling,the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel.It is found that ponderomotive self-channeling results in the emergence of a solitary wave and catastrophic focusing,which apparently decreases the region for stable propagation in a parameter space of laser power and the ratio of the initial laser spot radius to the channel radius(RLC).Direct numerical simulation confirms the theory of constant propagation,periodic defocusing and focusing oscillations in the parameter space,and reveals a radial instability which prevents the formation of bright and dark solitary waves.The corresponding unstable critical curve is added in the parameter space numerically and the induced unstable region above the unstable critical curve covers that of catastrophic focusing,which shrinks the stable region for laser beams.For the expected constant propagation,the results reveal the need for a low RLC.Further study illustrates that the channel power-law exponent has an obvious effect on the final stable region and laser propagation,for example increasing this exponent can enlarge the stable region significantly,which is beneficial for guiding of the laser and increases the lowest RLC for constant propagation.Our results also show that the initial laser amplitude has an apparent influence on the propagation behavior.

Propagation dynamics and experimental observation of quadratic vortex beam

The concept of a quadratic vortex beam is proposed, in which phase term of the beam is given by exp（i mθ2）. The phase of the quadratic vortex beam increases with azimuthal angle nonlinearly. This change in phase produces several unexpected effects. Unlike the circularly symmetric beam spot of normal vortex beams, the intensity distribution of the quadratic vortex beam is shown to be asymmetric. The phase singularities will shift in the transverse beam plane on propagation.

Important edge identification in complex networks based on local and global features

Identifying important nodes and edges in complex networks has always been a popular research topic in network science and also has important implications for the protection of real-world complex systems.Finding the critical structures in a system allows us to protect the system from attacks or failures with minimal cost.To date,the problem of identifying critical nodes in networks has been widely studied by many scholars,and the theory is becoming increasingly mature.However,there is relatively little research related to edges.In fact,critical edges play an important role in maintaining the basic functions of the network and keeping the integrity of the structure.Sometimes protecting critical edges is less costly and more flexible in operation than just focusing on nodes.Considering the integrity of the network topology and the propagation dynamics on it,this paper proposes a centrality measure based on the number of high-order structural overlaps in the first and second-order neighborhoods of edges.The effectiveness of the metric is verified by the infection-susceptibility(SI)model,the robustness index R,and the number of connected branchesθ.A comparison is made with three currently popular edge importance metrics from two synthetic and four real networks.The simulation results show that the method outperforms existing methods in identifying critical edges that have a significant impact on both network connectivity and propagation dynamics.At the same time,the near-linear time complexity can be applied to large-scale networks.

Study on the Two-Dimensional Density Distribution for Gas Plasmas Driven by Laser Pulse

We perform an experimental study of two-dimensional（2D） electron density profiles of the laser-induced plasma plumes in air by ordinarily laboratorial interferometry. The electron density distributions measured show a feature of hollow core. To illustrate the feature, we present a theoretical investigation by using dynamics analysis. In the simulation, the propagation of laser pulse with the evolution of electron density is utilized to evaluate ionization of air target for the plasma-formation stage. In the plasma-expansion stage, a simple adiabatic fluid dynamics is used to calculate the evolution of plasma outward expansion. The simulations show good agreements with experimental results, and demonstrate an effective way of determining 2D density profiles of the laser-induced plasma plume in gas.

Steady-state growing crack-tip field characteristics of mode Ⅲ elastic-viscoplastic/rigid interface cracks

The existence of viscosity effect at the interface of double dissimilar materials has an important impact on the distribution of the interface crack-tip field and the properties variety of the interface itself. The singularity and viscosity are considered in the crack-tip. The elastic-viscoplastic governing equations of double dissimilar materials at the interface crack-tip field are established. The displacement potential function and boundary condition of interface crack-tip are introduced. The numerical analysis of elastic-viscoplastic/rigid interface for mode Ⅲis worked out. The stress-strain fields are obtained at the crack-tip and the variation rules of solutions are discussed according to each parameter. The numerical results show that the viscosity effect is a main factor of the interface propagating in the crack-tip field, and the interface crack-tip is a viscoplastic field governed by the viscosity coefficient, Mach number （Ma）, and singularity exponent.

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.

Dynamic system uncertainty propagation using polynomial chaos

The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.