Showing papers on "Shock (mechanics) published in 2006"

Sub-Cell Shock Capturing for Discontinuous Galerkin Methods

Abstract: A shock capturing strategy for higher order Discontinuous Galerkin approximations of scalar conservation laws is presented. We show how the original explicit artificial viscosity methods proposed over fifty years ago for finite volume methods, can be used very eectively in the context of high order approximations. Rather than relying on the dissipation inherent in Discontinuous Galerkin approximations, we add an artificial viscosity term which is aimed at eliminating the high frequencies in the solution, thus eliminating Gibbs-type oscillations. We note that the amount of viscosity required for stability is determined by the resolution of the approximating space and therefore decreases with the order of the approximating polynomial. Unlike classical finite volume artificial viscosity methods, where the shock is spread over several computational cells, we show that the proposed approach is capable of capturing the shock as a sharp, but smooth profile, which is typically contained within one element. The method is complemented with a shock detection algorithm which is based on the rate of decay of the expansion coecients of the solution when this is expressed in a hierarchical orthonormal basis. For the Euler equations, we consider and discuss the performance of several forms of the artificial viscosity term.

Space and time organization in a shock-induced separated boundary layer

Abstract: The interaction of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.3 is experimentally investigated for a wide range of shock intensities. Characteristic time and length scales of the unsteady reflected shock and inside the downstream interaction region are obtained and compared with already existing results obtained in compression ramp experiments as well as in subsonic detached flows. Dimensionless characteristic frequencies are highlighted to characterize low-frequency shock unsteadiness as well as the different large scales which develop inside the initial part of the interaction. The possibility of describing the spatial development of the large scales inside the interaction zone using a mixing-layer scheme including compressibility effects is tested for a wide range of Mach numbers, shock intensities and geometrical configurations. Moreover, strong evidence of a statistical link between low-frequency shock movements and the downstream interaction is given. Finally, the downstream evolution of the structures shed into the boundary layer is characterized and shows features specific of our configuration.

Shock Ignition of Thermonuclear Fuel with High Areal Density

Abstract: A novel method by C. Zhou and R. Betti [Bull. Am. Phys. Soc. 50, 140 (2005)] to assemble and ignite thermonuclear fuel is presented. Massive cryogenic shells are first imploded by direct laser light with a low implosion velocity and on a low adiabat leading to fuel assemblies with large areal densities. The assembled fuel is ignited from a central hot spot heated by the collision of a spherically convergent ignitor shock and the return shock. The resulting fuel assembly features a hot-spot pressure greater than the surrounding dense fuel pressure. Such a nonisobaric assembly requires a lower energy threshold for ignition than the conventional isobaric one. The ignitor shock can be launched by a spike in the laser power or by particle beams. The thermonuclear gain can be significantly larger than in conventional isobaric ignition for equal driver energy.

Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics

Abstract: A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

Shock Effects in Meteorites

Abstract: Shock waves have played an important role in the history of virtually all meteorites All models of the early solar system invoke condensation of mineral grains, aggregation of grains to form small bodies, and aggregation of most of the small bodies to form planets The remaining small bodies, the asteroids, are accepted as the source of most meteorites Throughout the history of the solar system, these small bodies have repeatedly collided with one another and with the planets Since collisions produce shock waves in the colliding bodies, an understanding of shock wave effects is important to unraveling the impact history of the solar system as it is revealed in meteorites This chapter was originally intended as an update of the chapter by Stoffler et al (1988) Rather than update that chapter, which relies heavily on laboratory shock-recovery experiments in the interpretation of shock effects in meteorites, we have decided to take a different approach Here we emphasize the use of static high-pressure data on phase equilibria together with shock wave and thermal physics calculations to interpret observed microstructures of shocked meteorites A number of papers published during the past ten years have shown that this approach can yield new insights on the impact history of meteorites (Chen et al, 1996, 2004b; Sharp et al, 1997; Langenhorst and Poirier, 2000a; Xie and Sharp, 2000, 2004; Xie et al, 2002, 2005; DeCarli et al, 2004; Beck et al, 2004, 2005; Ohtani et al, 2004) One requirement for use of this approach is that some knowledge of shock wave physics is required Most general articles on shock wave physics do not present the information in a way that is useful to a reader who has been primarily trained in geology or mineralogy One of the objectives of this chapter is to present a useful tutorial on shock waves and shock wave calculations, including shock temperature and postshock temperature calculations Our emphasis is on simple techniques and useful approximations rather than mathematical rigor We will even attempt to present simple explanations of complicated phenomena, such as the quasichaotic nature of shock propagation in heterogeneous and/or porous materials We also present examples to illustrate how the principles of shock wave and thermal physics may be used to interpret the history of naturally shocked materials and how the occurrences and formation mechanisms of high-pressure minerals in meteorites can be used to constrain shock pressures 2 BACKGROUND

Non-linear particle acceleration at non-relativistic shock waves in the presence of self-generated turbulence

Abstract: Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This non-linear process adds to the non-linear modification of the shock due to the dynamical reaction of the accelerated particles on the shock. Building on a previous general solution of the problem of particle acceleration with arbitrary diffusion coefficients, we present here the first semi-analytical calculation of particle acceleration with both effects taken into account at the same time; charged particles are accelerated in the background of Alfven waves that they generate due to the streaming instability, and modify the dynamics of the plasma in the shock vicinity.

Particle acceleration at perpendicular shock waves: Model and observations

Abstract: Received 7 November 2005; revised 17 February 2006; accepted 27 February 2006; published 23 June 2006. [1] On the basis of a recently developed nonlinear guiding center theory for the perpendicular spatial diffusion coefficient k? used to describe the transport of energetic particles, we construct a model for diffusive particle acceleration at highly perpendicular shocks, i.e., shocks whose upstream magnetic field is almost orthogonal to the shock normal. We use k? to investigate energetic particle anisotropy and injection energy at shocks of all obliquities, finding that at 1 AU, for example, parallel and perpendicular shocks can inject protons with equal facility. It is only at highly perpendicular shocks that very high injection energies are necessary. Similar results hold for the termination shock. Furthermore, the inclusion of self-consistent wave excitation at quasiparallel shocks in evaluating the particle acceleration timescale ensures that it is significantly smaller than that for highly perpendicular shocks at low to intermediate energies and comparable at high energies. Thus higher proton energies are achieved at quasiparallel rather than highly perpendicular interplanetary shocks within 1 AU. However, both injection energy and the acceleration timescale at highly perpendicular shocks are sensitive to assumptions about the ratio of the two-dimensional (2-D) correlation length scale to the slab correlation length scale l2D/lk. Model proton spectra and intensity profiles accelerated by a highly perpendicular interplanetary shock are compared to an identical but parallel interplanetary shock, revealing important distinctions. Finally, we present observations of highly perpendicular interplanetary shocks that show that the absence of upstream wave activity does not inhibit particle acceleration at a perpendicular shock. The accelerated particle distributions closely resemble those expected of diffusive shock acceleration, and observed at oblique shocks, an example of which is shown.

Skin Friction and Heat Flux Measurements in Shock Boundary Layer Interaction Flows

Abstract: Modern nonintrusive techniques are used to make skin-friction and heat transfer measurements in two shockwave/turbulent boundary-layer interactions (SWTBLIs). The two-dimensional SWTBLI is generated by impingement of an incident oblique shock wave on a flat-plate boundary layer. The three-dimensional SWTBLI results from the interaction of the swept shock generated by a fin with a flat-plate boundary layer. The measurements are made using the global interferometry skin-friction technique for the skin friction and the quantitative infrared thermography technique for the heat transfer rate. The results show that, for the two- and three-dimensional interactions, there is a clear difference in the behavior of skin friction and heat transfer as the strength of the shock is changed. This observation suggests that the analogy between momentum and heat transfer, which is the basis of many simplified physical models, is not valid in SWTBLIs. These new data supplement the previous measurements that include boundary-layer properties, surface pressure distributions, and patterns of the limiting streamlines. Taken together, these data complete a data set that is suited for computational fluid dynamics validation.

The Effects of a Local Interstellar Magnetic Field on Voyager 1 and 2 Observations

Abstract: We show that an interstellar magnetic field can produce a north-south asymmetry in the solar wind termination shock Using Voyager 1 and 2 measurements, we suggest that the angle α between the interstellar wind velocity and the magnetic field is 30° < α < 60° The distortion of the shock is such that termination shock particles could have streamed outward along the spiral interplanetary magnetic field connecting Voyager 1 to the shock when the spacecraft was within ~2 AU of the shock The shock distortion is larger in the southern hemisphere, and Voyager 2 could be connected to the shock when it is within ~5 AU of the shock, but with particles from the shock streaming inward along the field Tighter constraints on the interstellar magnetic field should be possible when Voyager 2 crosses the shock in the next several years

3-D FEM simulation of laser shock processing

Abstract: Laser shock processing is an innovative surface treatment technique similar to shot peening. It can impart compressive residual stresses in material for improving fatigue, corrosion and wear resistance of metals. FEM simulation is an effective method to predict mechanical effects induced in the material treated by laser shock processing. An analysis procedure including dynamic analysis performed by LS-DYNA and static analysis performed by ANSYS is presented in detail to attain the simulation of the single and multiple laser shock processing to predict the residual stress field and the surface deformation. History of the energies during dynamic analysis is analyzed and validated by the theoretical calculation. The predicted residual stress field for single laser shock processing is well correlated with the available experimental data and a homogeneous depression with little roughness modification in the action zone of the shock pressure is induced on the treated surface according to the simulation of surface deformation. Simulation of multiple laser shocks is also performed, which indicates that compressive residual stresses and plastically affected depth can be extensively increased and gradually reach the saturated state with the increase of laser shock number.

Dynamic plasticity and failure of high-purity alumina under shock loading.

Abstract: Most high-performance ceramics subjected to shock loading can withstand high failure strength and exhibit significant inelastic strain that cannot be achieved under conventional loading conditions. The transition point from elastic to inelastic response prior to failure during shock loading, known as the Hugoniot elastic limit (HEL), has been widely used as an important parameter in the characterization of the dynamic mechanical properties of ceramics1,2,3,4. Nevertheless, the underlying micromechanisms that control HEL have been debated for many years. Here we show high-resolution electron microscopy of high-purity alumina, soft-recovered from shock-loading experiments. The change of deformation behaviour from dislocation activity in the vicinity of grain boundaries to deformation twinning has been observed as the impact pressures increase from below, to above HEL. The evolution of deformation modes leads to the conversion of material failure from an intergranular mode to transgranular cleavage, in which twinning interfaces serve as the preferred cleavage planes.

An explanation of the Voyager paradox: Particle acceleration at a blunt termination shock

Abstract: [1] Voyager 1 recently crossed the termination shock at the edge of our heliosphere. In contrast to the expectations of essentially all prior models, however, Voyager 1 did not observe the source of Anomalous Cosmic Rays (ACRs) as had been widely anticipated. We show here that the dearth of higher energy particles near the nose of the heliosphere is a natural consequence of the magnetic geometry in the region ahead of a flattened shock. Particle energization happens primarily back along the flanks of the shock where the injection energy is lower and where the magnetic field has had progressively longer connection times to accelerate particles. In addition to explaining the most baffling aspects of the Voyager 1 observations, this paradigm makes explicit predictions about what should be observed when Voyager 2 reaches the termination shock, significantly further back from its nose.

Solder-joint reliability in electronics under shock and vibration using explicit finite-element sub-modeling

Abstract: In this paper, the modeling approaches for first-level solder interconnects in shock and drop of electronics assemblies have been developed without any assumptions of geometric-symmetry or loading symmetry. The problem involves multiple scales from macro-scale transient-dynamics of electronic assembly to micro-structural damage history of interconnects. Previous modeling approaches include, solid-to-solid sub-modeling (Zhu et. al., 2001) using a half test PCB board, shell-to-solid sub-modeling technique using a quarter-symmetry model (Ren et. al., 2003; 2004). Inclusion of model symmetry in state-of-art models saves computational time, but targets primarily symmetric mode shapes. The modeling approach proposed in this paper enables prediction of both symmetric and anti-symmetric modes, which may dominate an actual drop-event. Approaches investigated include, smeared property models, Timoshenko-beam element models, explicit sub-models, and continuum-shell models. Transient dynamic behavior of the board assemblies in free and JEDEC-drop has been measured using high-speed strain and displacement measurements. Model predictions have been correlated with experimental data.

Effects of a Local Interstellar Magnetic Field on Voyager 1 and 2 Observations

Abstract: We show that that an interstellar magnetic field can produce a north/south asymmetry in solar wind termination shock. Using Voyager 1 and 2 measurements, we suggest that the angle $\alpha$ between the interstellar wind velocity and magnetic field is $30^{\circ} < \alpha < 60^{\circ}$. The distortion of the shock is such that termination shock particles could stream outward along the spiral interplanetary magnetic field connecting Voyager 1 to the shock when the spacecraft was within $\sim 2~AU$ of the shock. The shock distortion is larger in the southern hemisphere, and Voyager 2 could be connected to the shock when it is within $\sim 5~AU$ of the shock, but with particles from the shock streaming inward along the field. Tighter constraints on the interstellar magnetic field should be possible when Voyager 2 crosses the shock in the next several years.

Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces.

Abstract: There is strong experimental evidence for the existence of strange modes of failure of microelectromechanical systems (MEMS) devices under mechanical shock and impact. Such failures have not been explained with conventional models of MEMS. These failures are characterized by overlaps between moving microstructures and stationary electrodes, which cause electrical shorts. This work presents modeling and simulation of MEMS devices under the combination of shock loads and electrostatic actuation, which sheds light on the influence of these forces on the pull-in instability. Our results indicate that the reported strange failures can be attributed to early dynamic pull-in instability. The results show that the combination of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock alone or electrostatic actuation alone. In this work, a single-degree-of-freedom model is utilized to investigate the effect of the shock–electrostatic interaction on the response of MEMS devices. Then, a reduced-order model is used to demonstrate the effect of this interaction on MEMS devices employing cantilever and clamped–clamped microbeams. The results of the reduced-order model are verified by comparing with finite-element predictions. It is shown that the shock–electrostatic interaction can be used to design smart MEMS switches triggered at a predetermined level of shock and acceleration.

Observation of collapsing radiative shocks in laboratory experiments

Abstract: This article reports the observation of the dense, collapsed layer produced by a radiative shock in a laboratory experiment. The experiment uses laser irradiation to accelerate a thin layer of solid-density material to above 100km∕s, the first to probe such high velocities in a radiative shock. The layer in turn drives a shock wave through a cylindrical volume of Xe gas (at ∼6mg∕cm3). Radiation from the shocked Xe removes enough energy that the shocked layer increases in density and collapses spatially. This type of system is relevant to a number of astrophysical contexts, providing the potential to observe phenomena of interest to astrophysics and to test astrophysical computer codes.

Health monitoring for damage initiation & progression during mechanical shock in electronic assemblies

Abstract: Electronic products may be subjected shock and vibration during shipping, normal usage and accidental drop. High-strain rate transient bending produced by such loads may result in failure of fine-pitch electronics. Current experimental techniques rely on electrical resistance for determination of failure. Significant advantage can be gained by prior knowledge of impending failure for applications where the consequences of system failure may be catastrophic. This research effort focuses on an alternate approach to damage-quantification in electronic assemblies subjected to shock and vibration, without testing for electrical continuity. The proposed approach can be extended to monitor product-level damage. In this paper, statistical pattern recognition and leading indicators of shock-damage have been used to study the damage initiation and progression in shock and drop of electronic assemblies. Statistical pattern recognition is currently being employed in a variety of engineering and scientific disciplines such as biology, psychology, medicine, marketing, artificial intelligence, computer vision and remote sensing based in Jain, et. al. (2000). The application quantification of shock damage in electronic assemblies is new. Previously, free vibration of rectangular plates has been studied by various researchers as presented in Leissa (1969), Young (1950), Gorman (1982), Gurgoze (1984), and Wu (2003) for development of analytical closed-form models. In this paper, closed-form models have been developed for the eigen-frequencies and mode-shapes of electronic assemblies with various boundary conditions and component placement configurations. Model predictions have been validated with experimental data from modal analysis. Pristine configurations have been perturbed to quantify the degradation in confidence values with progression of damage. Sensitivity of leading indicators of shock-damage to subtle changes in boundary conditions, effective flexural rigidity, and transient strain response has been quantified. A damage index for experimental damage monitoring has been developed using the failure indicators. The above damage monitoring approach is not based on electrical continuity and hence can be applied to any electronic assembly structure irrespective of the interconnections. The damage index developed provides parametric damage progression data, thus removing the limitation of current failure testing, where the damage progression can not be monitored. Hence the proposed method does not require the assumption that the failure occurs abruptly after some number of drops and can be extended to product level drops.

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

Abstract: We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach’s experiment for the compressible Euler system, i. e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.

Simulation of shock-induced plasticity including homogeneous and heterogeneous dislocation nucleations

Abstract: A model of plasticity that couples discrete dislocation dynamics and finite element analysis is used to investigate shock-induced dislocation nucleation in copper single crystals. Homogeneous nucleation of dislocations is included based on large-scale atomistic shock simulations. The resulting prodigious rate of dislocation production takes the uniaxialy compressed material to a hydrostatically compressed state after a few tens of picoseconds. The density of dislocations produced in a sample with preexisting dislocation sources decreases slightly as shock rise time increases, implying that relatively lower densities would be expected for isentropic loading using extremely long rise times as suggested experimentally.

On the Efficiency of Fermi Acceleration at Relativistic Shocks

Abstract: We show that Fermi acceleration at an ultrarelativistic shock wave cannot operate on a particle for more than 1 Fermi cycles (i.e., u ? d ? u ? d) if the particle's Larmor radius is much smaller than the coherence length of the magnetic field on both sides of the shock, as is usually assumed. This conclusion proves to be in excellent agreement with recent numerical simulations. We thus argue that efficient Fermi acceleration at ultrarelativistic shock waves requires significant nonlinear processing of the far-upstream magnetic field with strong amplification of the small-scale magnetic power. The streaming or transverse Weibel instabilities are likely to play a key role in this respect.