Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Additional information can be obtained from http://gershwin.msd.anl.gov/theor

Unified force law for granular impact cratering

Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events and to probe the unusual nature of the granular state of matter. Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed; linear in speed; constant, proportional to the initial impact speed; and proportional to depth. This is reminiscent of high-speed ballistics impact in the 19th and 20th centuries, when a plethora of empirical rules were proposed. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 us precision. For a 1-inch diameter steel sphere dropped from a wide range of heights into non-cohesive glass beads, we reproduce prior observations either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between projectile and medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, while fundamentally different from that of liquids and solids, can be simply understood

Crack Front Waves and the dynamics of a rapidly moving crack

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport energy, generate surface structure and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to crack instabilities, yields both inhomogeneity and scaling behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure

Time resolved particle dynamics in granular convection

We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists mainly of vertical jumps, and a global ordered drift. The analysis of the system movement as a whole reveals that the observed bifurcation in the flight time is not adequately described by the Inelastic Bouncing Ball Model. Near the bifurcation point, friction plays and important role, and the branches of the bifurcation do not diverge as the control parameter is increased. We quantify the friction of the beads against the walls, showing that this interaction is the underlying mechanism responsible for the dynamics of the flow observed near the lateral wall

Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication

Time resolved particle dynamics in granular convection

We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists mainly of vertical jumps, and a global ordered drift. The analysis of the system movement as a whole reveals that the observed bifurcation in the flight time is not adequately described by the Inelastic Bouncing Ball Model. Near the bifurcation point, friction plays an important role, and the branches of the bifurcation do not diverge as the control parameter is increased. By fitting the grains trajectories near the wall it is possible to quantify the effective acceleration acting on them. A comparison of the mass centre flying time and the flying time determined for the grains near the wall exposes the underlying mechanism that causes the downward flow

Elastic forces that do no work and the dynamics of fast cracks

Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is used to propose a universal scenario, in which three dimensionality is essential, for the dynamic instability of fast cracks in thin brittle materials.Comment: 8 pages Latex, 1 Postscript figur

Far-Infrared to Millimeter Astrophysical Dust Emission. II: Comparison of the Two-Level Systems (TLS) model with Astronomical Data

In a previous paper we proposed a new model for the emission by amorphous astronomical dust grains, based on solid-state physics. The model uses a description of the Disordered Charge Distribution (DCD) combined with the presence of Two-Level Systems (TLS) defects in the amorphous solid composing the grains. The goal of this paper is to confront this new model to astronomical observations of different Galactic environments in the FIR/submm, in order to derive a set of canonical model parameters to be used as a Galactic reference to be compared to in future Galactic and extragalactic studies. We confront the TLS model with existing astronomical data. We consider the average emission spectrum at high latitudes in our Galaxy as measured with FIRAS and WMAP, as well as the emission from Galactic compact sources observed with Archeops, for which an inverse relationship between the dust temperature and the emissivity spectral index has been evidenced. We show that, unlike models previously proposed which often invoke two dust components at different temperatures, the TLS model successfully reproduces both the shape of the Galactic SED and its evolution with temperature as observed in the Archeops data. The best TLS model parameters indicate a charge coherence length of \simeq 13 nm and other model parameters in broad agreement with expectations from laboratory studies of dust analogs. We conclude that the millimeter excess emission, which is often attributed to the presence of very cold dust in the diffuse ISM, is likely caused solely by TLS emission in disordered amorphous dust grains. We discuss the implications of the new model, in terms of mass determinations from millimeter continuum observations and the expected variations of the emissivity spectral index with wavelength and dust temperature. The implications for the analysis of the Herschel and Planck satellite data are discussed.Comment: Accepted for publication in A&A (16 pages, 9 figures, 6 tables