Gil Cohen | Weizmann Institute of Science (original) (raw)

Papers by Gil Cohen

International Journal of Fracture, 2006

We perform real-time measurements of the net contact area between two blocks of like material at ... more We perform real-time measurements of the net contact area between two blocks of like material at the onset of frictional slip. We show that the process of interface detachment, which immediately precedes the inception of frictional sliding, is governed by three different types of detachment fronts. These cracklike detachment fronts differ by both their propagation velocities and by the amount of net contact surface reduction caused by their passage. The most rapid fronts propagate at intersonic velocities but generate a negligible reduction in contact area across the interface. Sub-Rayleigh fronts are crack-like modes which propagate at velocities up to the Rayleigh wave speed, V , and give rise to an approximate 10% reduction in net contact area. The most efficient contact area reduction (~20%) is precipitated by the passage of "slow detachment fronts". These fronts propagate at "anomalously" slow velocities, which are over an order of magnitude lower than V yet orders of magnitude higher than other characteristic velocity scales such as either slip or loading velocities. Slow fronts are generated, in conjunction with intersonic fronts, by the sudden arrest of sub-Rayleigh fronts. No overall sliding of the interface occurs until either of the slower two fronts traverses the entire interface, and motion at the leading edge of the interface is initiated. Slip at the trailing edge of the interface accompanies the motion of both the slow and sub-Rayleigh fronts. We might expect these modes to be important in both fault nucleation and earthquake dynamics. R R

Tribology Letters, 2010

We present an experimental study of the onset of local frictional motion along a long, spatially ... more We present an experimental study of the onset of local frictional motion along a long, spatially extended interface that separates two PMMA blocks in dry frictional contact. At applied shear forces significantly below the static friction threshold, rapid precursory detachment fronts are excited, which propagate at near sound speeds along the interface. These fronts initiate from the interface edge and arrest prior to traversing the entire sample length. Along the fronts’ path, we perform real-time measurements of the real contact area at every spatial point within the interface. In addition, the motion (slip) of the material adjacent to the interface is simultaneously measured at chosen locations. Upon their arrival at each spatial point along their path, these fronts instantaneously (within 4 μs) reduce the net contact area. Net slip is only initiated after this contact area reduction occurs. Slip is initially rapid and progresses at its initial velocity for a constant (60 μs) duration. Slip dynamics then undergo a sharp transition to velocities an order of magnitude slower, which remain nearly constant until slip arrest. We demonstrate that this scenario can be quantitatively explained by a model of interface weakening caused by instantaneous fracture-induced heating. Sustained rapid slip occurs in this weakened phase. Once the interface cools beneath its glass temperature the sharp transition to slow slip takes place. A similar fracture-induced weakening scenario might be expected in additional classes of materials.

International Journal of Fracture, 2003

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an i... more A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack’s propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a ‘crack front’). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially ‘massless’ cracks acquire inertia.

Science, 2010

The way in which a frictional interface fails is critical to our fundamental understanding of fai... more The way in which a frictional interface fails is critical to our fundamental understanding of failure processes in fields ranging from engineering to the study of earthquakes. Frictional motion is initiated by rupture fronts that propagate within the thin interface that separates two sheared bodies. By measuring the shear and normal stresses along the interface, together with the subsequent rapid real-contact-area dynamics, we find that the ratio of shear stress to normal stress can locally far exceed the static-friction coefficient without precipitating slip. Moreover, different modes of rupture selected by the system correspond to distinct regimes of the local stress ratio. These results indicate the key role of nonuniformity to frictional stability and dynamics with implications for the prediction, selection, and arrest of different modes of earthquakes.

International Journal of Fracture, 2003

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an i... more A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack's propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a `crack front'). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially `massless' cracks acquire inertia.

Journal of Geophysical Research, 2006

1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory exper... more 1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory experiments in which artificial rock slabs are fractured under uniaxial tension. By performing detailed measurements of the instantaneous fracture velocity and the fracture surface topography, we quantitatively relate fracture morphology with the dynamics of the surface formation. We show that fracture dynamics in these materials is strongly influenced by the interaction of the fracture front with material heterogeneities and by the formation of microbranches. The instantaneous fracture velocity is characterized by abrupt fluctuations, whose amplitudes increase with the average velocity and which are correlated with the surface roughness. The surfaces of the fractures display aligned grooves and ridges, which extend large distances in the propagation direction and are localized in the transverse direction. These features, interpreted as lines of aligned microbranches, are observed solely when the fracture velocity is above 0.3 of the Rayleigh wave speed. In addition, small-scale striations corresponding to fracture front waves are identified. The overall similarity between fracture dynamics in these heterogeneous materials and those in ideal amorphous materials suggests that universal processes control the dynamics. The heterogeneity of the grainy medium, however, strongly amplifies the velocity fluctuations and enhances both the deflection and segmentation of fracture fronts.

Physical Review Letters, 2010

We experimentally investigate how disorder comes about in parametrically excited waves on a fluid... more We experimentally investigate how disorder comes about in parametrically excited waves on a fluid surface (Faraday waves). We find that the transition from an ordered pattern to disorder corresponding to ''defect-mediated turbulence'' is mediated by a spatially incoherent oscillatory phase. This phase consists of highly damped waves that propagate through the effectively elastic lattice defined by the pattern. They have a well-defined frequency, velocity, and transverse polarization. As these waves decay within a few lattice spaces, they are spatially and temporally uncorrelated at larger scales.

Journal of Geophysical Research, 2006

1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory exper... more 1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory experiments in which artificial rock slabs are fractured under uniaxial tension. By performing detailed measurements of the instantaneous fracture velocity and the fracture surface topography, we quantitatively relate fracture morphology with the dynamics of the surface formation. We show that fracture dynamics in these materials is strongly influenced by the interaction of the fracture front with material heterogeneities and by the formation of microbranches. The instantaneous fracture velocity is characterized by abrupt fluctuations, whose amplitudes increase with the average velocity and which are correlated with the surface roughness. The surfaces of the fractures display aligned grooves and ridges, which extend large distances in the propagation direction and are localized in the transverse direction. These features, interpreted as lines of aligned microbranches, are observed solely when the fracture velocity is above 0.3 of the Rayleigh wave speed. In addition, small-scale striations corresponding to fracture front waves are identified. The overall similarity between fracture dynamics in these heterogeneous materials and those in ideal amorphous materials suggests that universal processes control the dynamics. The heterogeneity of the grainy medium, however, strongly amplifies the velocity fluctuations and enhances both the deflection and segmentation of fracture fronts.

We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous m... more We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous materials. We first compare the dynamic behavior of "standard" brittle materials (e.g. glass) with the corresponding features observed in "model" materials, polyacrylamide gels, in which the relevant sound speeds can be reduced by 2-3 orders of magnitude. The results of this comparison indicate universality in many aspects of dynamic fracture in which these highly different types of materials exhibit identical behavior. Observed characteristic features include the existence of a critical velocity beyond which frustrated crack branching occurs 1, 2 and the profile of the micro-branches formed. We then go on to examine the behavior of the leading edge of the propagating crack, when this 1D "crack front" is locally perturbed by either an externally introduced inclusion or, dynamically, by the generation of a micro-branch. Comparison of the behavior of the excited fronts in both gels and in soda-lime glass reveals that, once again, many aspects of the dynamics of these excited fronts in both materials are identical. These include both the appearance and character of crack front inertia and the generation of "Front Waves", which are coherent localized waves 3-6 which propagate along the crack front. Crack front inertia is embodied by the appearance of a "memory" of the crack front 7,8 , which is absent in standard 2D descriptions of fracture. The universality of these unexpected inertial effects suggests that a qualitatively new 3D description of the fracture process is needed, when the translational invariance of an unperturbed crack front is broken.

Nature, 2004

the other hand, the basic 4a 0 £ 4a 0 checkerboard state with its 4/3a 0 £ 4/3a 0 modulations and... more the other hand, the basic 4a 0 £ 4a 0 checkerboard state with its 4/3a 0 £ 4/3a 0 modulations and pseudogap variations changes subtly so that the A(R, E) (insets in ) appear very similar between dopings. Thus, the checkerboard electronic state appears for x # 0.08 in the ZTPG regime but continues to exist for p . p SC , the critical doping for superconductivity.

Electronic Colloquium on Computational Complexity, 2010

Electronic Colloquium on Computational Complexity, 2011

We study the following problem raised by von zur Gathen and Roche [GR97]:

We study the following problem raised by von zur Gathen and Roche [GR97]:

International Journal of Fracture, 2006

We perform real-time measurements of the net contact area between two blocks of like material at ... more We perform real-time measurements of the net contact area between two blocks of like material at the onset of frictional slip. We show that the process of interface detachment, which immediately precedes the inception of frictional sliding, is governed by three different types of detachment fronts. These cracklike detachment fronts differ by both their propagation velocities and by the amount of net contact surface reduction caused by their passage. The most rapid fronts propagate at intersonic velocities but generate a negligible reduction in contact area across the interface. Sub-Rayleigh fronts are crack-like modes which propagate at velocities up to the Rayleigh wave speed, V , and give rise to an approximate 10% reduction in net contact area. The most efficient contact area reduction (~20%) is precipitated by the passage of "slow detachment fronts". These fronts propagate at "anomalously" slow velocities, which are over an order of magnitude lower than V yet orders of magnitude higher than other characteristic velocity scales such as either slip or loading velocities. Slow fronts are generated, in conjunction with intersonic fronts, by the sudden arrest of sub-Rayleigh fronts. No overall sliding of the interface occurs until either of the slower two fronts traverses the entire interface, and motion at the leading edge of the interface is initiated. Slip at the trailing edge of the interface accompanies the motion of both the slow and sub-Rayleigh fronts. We might expect these modes to be important in both fault nucleation and earthquake dynamics. R R

Tribology Letters, 2010

We present an experimental study of the onset of local frictional motion along a long, spatially ... more We present an experimental study of the onset of local frictional motion along a long, spatially extended interface that separates two PMMA blocks in dry frictional contact. At applied shear forces significantly below the static friction threshold, rapid precursory detachment fronts are excited, which propagate at near sound speeds along the interface. These fronts initiate from the interface edge and arrest prior to traversing the entire sample length. Along the fronts’ path, we perform real-time measurements of the real contact area at every spatial point within the interface. In addition, the motion (slip) of the material adjacent to the interface is simultaneously measured at chosen locations. Upon their arrival at each spatial point along their path, these fronts instantaneously (within 4 μs) reduce the net contact area. Net slip is only initiated after this contact area reduction occurs. Slip is initially rapid and progresses at its initial velocity for a constant (60 μs) duration. Slip dynamics then undergo a sharp transition to velocities an order of magnitude slower, which remain nearly constant until slip arrest. We demonstrate that this scenario can be quantitatively explained by a model of interface weakening caused by instantaneous fracture-induced heating. Sustained rapid slip occurs in this weakened phase. Once the interface cools beneath its glass temperature the sharp transition to slow slip takes place. A similar fracture-induced weakening scenario might be expected in additional classes of materials.

International Journal of Fracture, 2003

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an i... more A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack’s propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a ‘crack front’). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially ‘massless’ cracks acquire inertia.

Science, 2010

The way in which a frictional interface fails is critical to our fundamental understanding of fai... more The way in which a frictional interface fails is critical to our fundamental understanding of failure processes in fields ranging from engineering to the study of earthquakes. Frictional motion is initiated by rupture fronts that propagate within the thin interface that separates two sheared bodies. By measuring the shear and normal stresses along the interface, together with the subsequent rapid real-contact-area dynamics, we find that the ratio of shear stress to normal stress can locally far exceed the static-friction coefficient without precipitating slip. Moreover, different modes of rupture selected by the system correspond to distinct regimes of the local stress ratio. These results indicate the key role of nonuniformity to frictional stability and dynamics with implications for the prediction, selection, and arrest of different modes of earthquakes.

International Journal of Fracture, 2003

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an i... more A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack's propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a `crack front'). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially `massless' cracks acquire inertia.

Journal of Geophysical Research, 2006

1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory exper... more 1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory experiments in which artificial rock slabs are fractured under uniaxial tension. By performing detailed measurements of the instantaneous fracture velocity and the fracture surface topography, we quantitatively relate fracture morphology with the dynamics of the surface formation. We show that fracture dynamics in these materials is strongly influenced by the interaction of the fracture front with material heterogeneities and by the formation of microbranches. The instantaneous fracture velocity is characterized by abrupt fluctuations, whose amplitudes increase with the average velocity and which are correlated with the surface roughness. The surfaces of the fractures display aligned grooves and ridges, which extend large distances in the propagation direction and are localized in the transverse direction. These features, interpreted as lines of aligned microbranches, are observed solely when the fracture velocity is above 0.3 of the Rayleigh wave speed. In addition, small-scale striations corresponding to fracture front waves are identified. The overall similarity between fracture dynamics in these heterogeneous materials and those in ideal amorphous materials suggests that universal processes control the dynamics. The heterogeneity of the grainy medium, however, strongly amplifies the velocity fluctuations and enhances both the deflection and segmentation of fracture fronts.

Physical Review Letters, 2010

We experimentally investigate how disorder comes about in parametrically excited waves on a fluid... more We experimentally investigate how disorder comes about in parametrically excited waves on a fluid surface (Faraday waves). We find that the transition from an ordered pattern to disorder corresponding to ''defect-mediated turbulence'' is mediated by a spatially incoherent oscillatory phase. This phase consists of highly damped waves that propagate through the effectively elastic lattice defined by the pattern. They have a well-defined frequency, velocity, and transverse polarization. As these waves decay within a few lattice spaces, they are spatially and temporally uncorrelated at larger scales.

Journal of Geophysical Research, 2006

1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory exper... more 1] The dynamics of rapid fracturing of heterogeneous grainy media are studied in laboratory experiments in which artificial rock slabs are fractured under uniaxial tension. By performing detailed measurements of the instantaneous fracture velocity and the fracture surface topography, we quantitatively relate fracture morphology with the dynamics of the surface formation. We show that fracture dynamics in these materials is strongly influenced by the interaction of the fracture front with material heterogeneities and by the formation of microbranches. The instantaneous fracture velocity is characterized by abrupt fluctuations, whose amplitudes increase with the average velocity and which are correlated with the surface roughness. The surfaces of the fractures display aligned grooves and ridges, which extend large distances in the propagation direction and are localized in the transverse direction. These features, interpreted as lines of aligned microbranches, are observed solely when the fracture velocity is above 0.3 of the Rayleigh wave speed. In addition, small-scale striations corresponding to fracture front waves are identified. The overall similarity between fracture dynamics in these heterogeneous materials and those in ideal amorphous materials suggests that universal processes control the dynamics. The heterogeneity of the grainy medium, however, strongly amplifies the velocity fluctuations and enhances both the deflection and segmentation of fracture fronts.

We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous m... more We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous materials. We first compare the dynamic behavior of "standard" brittle materials (e.g. glass) with the corresponding features observed in "model" materials, polyacrylamide gels, in which the relevant sound speeds can be reduced by 2-3 orders of magnitude. The results of this comparison indicate universality in many aspects of dynamic fracture in which these highly different types of materials exhibit identical behavior. Observed characteristic features include the existence of a critical velocity beyond which frustrated crack branching occurs 1, 2 and the profile of the micro-branches formed. We then go on to examine the behavior of the leading edge of the propagating crack, when this 1D "crack front" is locally perturbed by either an externally introduced inclusion or, dynamically, by the generation of a micro-branch. Comparison of the behavior of the excited fronts in both gels and in soda-lime glass reveals that, once again, many aspects of the dynamics of these excited fronts in both materials are identical. These include both the appearance and character of crack front inertia and the generation of "Front Waves", which are coherent localized waves 3-6 which propagate along the crack front. Crack front inertia is embodied by the appearance of a "memory" of the crack front 7,8 , which is absent in standard 2D descriptions of fracture. The universality of these unexpected inertial effects suggests that a qualitatively new 3D description of the fracture process is needed, when the translational invariance of an unperturbed crack front is broken.

Nature, 2004

the other hand, the basic 4a 0 £ 4a 0 checkerboard state with its 4/3a 0 £ 4/3a 0 modulations and... more the other hand, the basic 4a 0 £ 4a 0 checkerboard state with its 4/3a 0 £ 4/3a 0 modulations and pseudogap variations changes subtly so that the A(R, E) (insets in ) appear very similar between dopings. Thus, the checkerboard electronic state appears for x # 0.08 in the ZTPG regime but continues to exist for p . p SC , the critical doping for superconductivity.

Electronic Colloquium on Computational Complexity, 2010

Electronic Colloquium on Computational Complexity, 2011

We study the following problem raised by von zur Gathen and Roche [GR97]:

We study the following problem raised by von zur Gathen and Roche [GR97]: