Molecular dynamics simulation of plastic effects upon spalling

The molecular dynamics method is applied to simulate spalling during the plane shock interaction between plates. The effect of lattice defects in a material on the propagation of a shock wave and the process of spalling is studied. The plastic effects are described using a model of imperfect particle packing with defects (vacancies). The model proposed can describe the separation of the shock-wave front into an elastic precursor and a plastic front and give velocity profiles for the free target surface close to the experimental profiles.     

Wave velocities in shock-compressed cubic and hexagonal single crystals above the elastic limit

When solids are subjected to high-pressure shock-wave loading, multiple stress waves propagate with velocities dependent upon the elastic and inelastic compressibilities of the solid. The present paper shows that the inelastic or plastic waves in cubic and hexagonal single crystals do not necessarily propagate with the bulk sound speed as they do in isotropic elastic-plastic solids. This result is a consequence of anisotropy in the plastic deformation which depends on the slip plane orientation in the crystal and has important consequences with regard to the determination of compressibilities from shock-wave data. In particular, for wave propagation in the <110> directions of cubic crystals the departure from the bulk velocity can be significant (5–25 per cent). For wave propagation normal to the c-axis in hexagonal crystals, the plastic wave velocity also differs from the bulk sound speed (10–25 per cent). Plastic wave velocities are tabulated for a number of cubic crystals on the basis of the various slip systems common to these materials. The calculated velocities are then compared with experimental data on shock-loaded single-crystal aluminum and sodium chloride.     

Molecular dynamic studies on materials under laser shocks

Molecular dynamic (MD) simulations offer a powerful means of understanding the microscopic characteristics of shock-propagation through solids and fluids, especially for the short spatial and temporal scales relevant to laser-driven shocks. First-principles molecular dynamics can be directly compared with time-resolved experimental measurements, and methods based on empirical (embedded-atom) potentials fitted to first-principles quantum-mechanical calculations are effective for MD simulations of shock propagation through many millions of atoms. In comparison, thermodynamic approaches based on free-energy considerations do not provide detailed information about mechanical-relaxation or phase-transformation processes within the shock front. We illustrate these ideas by way of embedded-atom simulations of shock-wave propagation through copper crystals of different orientation.     

Dissipative processes under the shock compression of glass

New experimental data on the behavior of the K8 and TF1 glasses under shock-wave loading conditions are obtained. It is found that the propagation of shock waves is close to the self-similar one in the maximum compression stress range 4-12 GPa. Deviations from a general deformation diagram, which are related to viscous dissipation, take place when the final state of compression is approached. The parameter region in which failure waves form in glass is found not to be limited to the elastic compression stress range, as was thought earlier. The failure front velocity increases with the shock compression stress. Outside the region covered by a failure wave, the glasses demonstrate a high tensile dynamic strength (6-7 GPa) in the case of elastic compression, and this strength is still very high after transition through the elastic limit in a compression wave.     

Shape of a wave front in a heterogenous medium

Wave propagation in a heterogeneous medium, characterized by a distribution of local elastic moduli, is studied. Both acoustic and elastic waves are considered, as are spatially random and power-law correlated distributions of the elastic moduli with nondecaying correlations. Three models--a continuum scalar model, and two discrete models--are utilized. Numerical simulations indicate the existence, at all times, of the relation, alpha = H, where alpha is the roughness exponent of the wave front in the medium, and H is the Hurst exponent that characterizes the spatial correlations in the distribution of the local elastic moduli. Hence, a direct relation between the static morphology of an inhomogeneous correlated medium and its dynamical properties is established. In contrast, for a wave front in random media, alpha = 0 (logarithmic growth) at short times, followed by a crossover to the classical value, alpha = 1/2, at long times.     

Mass transport in metals under intensive impulse reactions

An unusually high mobility of atoms under intensive impulse reactions is explained by the behavior of point defects at the shock wave front. It is shown that either a shock wave front or moving dislocations can capture the interstitials, or they can be thermally activated in the direction of the shock wave propagation.     

Interaction of a planar gravitational wave with a scalar field

It is shown that a strong gravitational wave can reflect a flow of scalar particles moving toward it. The particles initially penetrate the forward wave propagation front and only then are reflected.     

Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture

We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.     

Additive noise induces front propagation

The effect of additive noise on a static front that connects a stable homogeneous state with an also stable but spatially periodic state is studied. Numerical simulations show that noise induces front propagation. The conversion of random fluctuations into direct motion of the front's core is responsible of the propagation; noise prefers to create or remove a bump, because the necessary perturbations to nucleate or destroy a bump are different. From a prototype model with noise, we deduce an adequate equation for the front's core. An analytical expression for the front velocity is deduced, which is in good agreement with numerical simulations.     

Coupled fluid–structure solver: The case of shock wave impact on monolithic and composite material plates

An unstructured adaptive mesh flow solver, a finite element structure solver and a moving mesh algorithm were implemented in the numerical simulation of the interaction between a shock wave and a structure. In the past, this interaction is mostly considered as one-way in the sense that the shock causes a transient load on the structure while it is reflected uneffected by the impact. A fully coupled approach was implemented in the present work which can account for the effects associated with a mutual interaction. This approach included a compressible flow Eulerian solver of second order accuracy in finite volume formulation for the fluid and a Langargian solver in finite element formulation for the solid structure. A novel implementation of advancing front moving mesh algorithm was made possible with the introduction of a flexible and efficient quad-edge data structure. Adaptive mesh refinement was introduced into the flow solver for improved accuracy as well. Numerical results are further validated by theoretical analysis, experimental data and results from other numerical simulations. Grid dependency study was performed and results showed that the physical phenomena and quantities were independent of the numerical grid chosen in the simulations. The results illuminated complicated flow phenomena and structure vibration patterns, which in order to be detected experimentally require capabilities beyond those of the current experimental techniques. The numerical simulations also successfully modelled the aero-acoustic damping effects on the structure, which do not exist in previous numerical models. Further analysis of the results showed that the mutual interaction is not linear and that the non-linearity arises because the wave propagation in the fluid is not linear and it cascades a non-linear and non-uniform loading on the plate. Non-linearity intensifies when the plate is vibrating at high frequency while the wave propagation speed is low.     

低渗透多孔介质非达西渗流动边界界面追踪

基于低渗透多孔介质非达西不稳定渗流的动边界数学模型,推导动边界移动速度的微分表达式,揭示动边界移动速度与动边界上地层压力关于径向距离的二次导数成正比;由此利用拉格朗日三点插值公式求得动边界附近控制方程的有限差分格式,并对下一时刻动边界的精确位置进行追踪.有限差分方法的数值结果表明界面追踪法可较好地反映低渗透多孔介质非达西不稳定渗流动边界的移动规律.     

Wave propagation in non-homogeneous thin elastic rods subjected to time dependent stress impact

The problem of wave propagation in a non-homogeneous elastic rod subjected to time dependent stress impact is considered. Similarity transformations are applied to the equation of motion of the rod and its boundary condition. Along with the similarity characteristic relationship on the moving front these are used to obtain the similarity representation as a boundary value problem. A closed form solution of the similarity representation is obtained and, in addition, restrictions on the parameters and relations among them are also obtained. Results for the stress distribution in the rod at a specific time are graphically represented in non-dimensional co-ordinates.     

Orientation dependence in molecular dynamics simulations of shocked single crystals

We use multimillion-atom molecular dynamics simulations to study shock wave propagation in fcc crystals. As shown recently, shock waves along the <100> direction form intersecting stacking faults by slippage along 111 close-packed planes at sufficiently high shock strengths. We find even more interesting behavior of shocks propagating in other low-index directions: for the <111> case, an elastic precursor separates the shock front from the slipped (plastic) region. Shock waves along the <110> direction generate a leading solitary wave train, followed (at sufficiently high shock speeds) by an elastic precursor, and then a region of complex plastic deformation.     

Bending of a strong-explosion-induced shock wave around a density singularity (as applied to the remnants of hypernovae)

The remnants of hypernovae, which can correspond to cosmological gamma-ray bursts, are analyzed on the basis of the Kompaneets equation in the strong explosion approximation. Exact solutions to the Kompaneets equation are obtained, and the shape of shock-wave fronts from a noncentral point explosion in a medium whose density decreases quadratically with the distance from the density singularity and tends to a constant at large distances. The bending of the shock-wave front around a density singularity is discussed. The results are compared with data on X-ray sources that can correspond to hypernovae.     

Elastoplastic behavior of marble, granite, and quartzite under shock compression

Profiles of elastoplastic shock waves were experimentally revealed in three rocks, namely, in marble (ρ₀=2.68 g/cm³), quartzite (ρ₀=2.65 g/cm³), and granite (ρ₀=2.63 g/cm³). In all these substances, the splittingof the shock-wave front into a leading elastic precursor and a following plastic compression wave wererevealed. A diffusion of the front of the elastic precursor and a decrease in its amplitude were found to occur asthe front propagates through the samples of the substances studied. No sharp decrease in the amplitude of elasticwaves (yielding “tooth”) was fixed. Pressures in the elastic and plastic compression waves, as well as the waveand mass velocities and the magnitudes of the relative compression were determined.     

Nonlinear Longitudinal Strain Waves in a Solid Exposed to Pulsed Laser Radiation

The propagation of longitudinal strain waves in a solid with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation, relaxation, and the strain-induced drift of defects and the flexoelectricity on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of both shock fronts and solitary waves (solitons). Exact solutions depending on the type of relation between the coefficients in the equation and describing both the shock-wave structures and the evolution of solitary waves are presented. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate and the flexoelectricity to linear elastic moduli and spatial dispersion are determined.     

Wave turbulence buildup in a vibrating plate

We report experimental and numerical results on the buildup of the energy spectrum in wave turbulence of a vibrating thin elastic plate. Three steps are observed: first a short linear stage, then the turbulent spectrum is constructed by the propagation of a front in wave number space and finally a long time saturation due to the action of dissipation. The propagation of a front at the second step is compatible with scaling predictions from the Weak Turbulence Theory.     

Observation of locked optical kink-antikink spatial shock waves

We report the first experimental observation of optical spatial shock-wave pairs. The shock waves consist of two coupled kink and antikink beams that remain locked to each other throughout propagation in a nonlinear diffusion-driven photorefractive crystal. These coupled shock-wave pairs move undistorted at angles that fall outside their original angular sector of propagation.