Propagation was a recurring theme throughout the conference both in the context of earthquake rupture and fracturing, and also in the context of the transition to the sliding mode of friction where the surfaces may rupture in a pulse-like or crack-like manner. A number of the talks given used examples specifically related to the earth systems under investigation (Rice, Dunham, Dmowska, Spudich, Madariaga, Ohnaka, Lapusta) others considered particular materials or structural systems (Z. Bazant, Wiederhorn, Bouchaud, Vanel, Ciliberto, Bonamy, Marder). There were a number of talks that approached the basic physics of propagation of failure using either atomistic methods (Marder, Bernstein) or coarse-grained physical theories (Karma, Brener, Spatschek, Wiese). Still other talks considered using materials systems as analogs for earthquake processes (Ravi-Chandar, Fineberg, Rosakis and Lapusta).

A number of presentations and discussions considered the various mechanisms that may operate during the nucleation of rupture including slow processes that accompany slow propagation of cracks. These included detailed analyses of thermal activation in disordered materials like paper and polymeric materials by Cilibertoand Vanel. Stress corrosion cracking was also investigated and the evidence for cavity formation during fracture was considered by Bouchaud, who observed cavity formation near surfaces during in situ AFM studies and Wiederhorn who sees no evidence for such cavities in post mortem studies of fracture surfaces. In the context of earthquakes the weakening mechanisms that could lead to nucleation were presented by Dieterich and Lapusta). Rice discussed the mechanisms of flash heating and pore pressurization in some detail. A number of discussions considered the role of pinning of propagating fronts and discussions lead by Wiese, Robbins and Dahmen considered whether these models might provide a simple physical model that shares some of the intermittency also seen in more complex systems like earthquakes.

There were a number of interesting talks describing research in various open problems in tensile (Mode I) fracture. Michael Marder and Noam Bernstein presented results describing the dynamic fracture of silicon. Marder compared experiments to molecular dynamics simulations, pointing out serious problems that exist in providing quantitative descriptions of even basic aspects of dynamic fracture with the potentials generally used in molecular dynamic simulations. Bernstein then demonstrated that much better quantitative agreement with experiments could be obtained using a quantum mechanical approach in the vicinity of the crack tip. More coarse-grained physical models were discussed by Alain Karma and Robert Spatschek. These talks centered on the dynamics of the process zone in the near-tip region of dynamic cracks. The talks by Karma and Spatschek described phase-field models of crack propagation. In phase-field models, a Ginzburg-Landau type description is used to regularize the stress-field singularity in the process zone surrounding a crack's tip. The phase field is then coupled to the surrounding linear elastic fields. Both models predict nontrivial crack-path criteria together with instabilities of dynamic cracks that occur at high propagation velocities.

Results in the fracture of amorphous materials were presented by Michael Marder and Cindy Rountree. Marder considered the dynamic fracture of rubber. By coupling Kelvin dissipation to the non-Hookean elastic response of rubber, experimentally observed intersonic, shock-like modes of propagation are theoretically described. Rountree studied the question of void-crack tip interactions at the atomic scale in amorphous silica. Her MD simulations of dynamic fracture yielded results qualitatively similar to Elizabeth Bouchaud's and Daniel Bonamy's experiments on the dynamics of slow stress-corrosion driven fracture. In these experiments the near tip zone of a slowly propagating crack was visualized by AFM (Bouchaud) and the scaling properties of the resulting fracture surface were described (Bonamy). Additional aspects of slow tensile fracture were presented by Tristan Baumberger, who described measurements of the velocity dependence of the fracture energy in soft hydro-gels at slow crack velocities.

The range of speeds at which a rupture propagates affects the resultant ground motion and is information needed for inverting seismographic information. In particular, the issue is when (and if) earthquake ruptures can propagate faster than a characteristic elastic wave speed of the surrounding material; for a homogeneous material, the relevant elastic wave speed is the Rayleigh wave speed. Ruptures that propagate faster than such a characteristic elastic wave speed are here termed `super-shear' ruptures. Thus, basic questions are what limits the speed of propagation of ruptures and what are the mechanisms that permit super-shear ruptures to occur. Rupture can be taken to mean eaither frictional sliding or shear fracture along along a fault or interface. There are common features between these so that both fracture and frictional sliding studies are relevant, but there may also be distinctions in behavior which are not yet fully characterized. Field observations of possible super-shear ruptures date back to the work of Archuleta (1984) and evidence for them has been increasing. Spudich discussed field observations and noted that the 2004 Parkfiled earthquake is the smallest earthquake for which supershear propagation has been observed. Some of the observations of the Parkfield earthquake are consistent with numerical predictions of Harris and Day (1997) and the laboratory experiments of Xia et al. (2005). Dunham discussed analyses of conditions for a transition from sub-Rayleigh propagation to super shear propagation and found that a supershear transition occurs when the stress field ahead of a rupture propagating at sub-Rayleigh speeds meets a nucleation criterion. This requires heterogeneities along the front. Coker presented analyses of frictional sliding along an interface between identical elastic solids under impact loading conditions and found three modes of propagation; a crack-like mode, a pulse-like mode and a mode involving a train of pulses. In some cases, propagation speeds faster than any characteristic elastic wave speed were found and mechanisms of transition were discussed along with characteristic features of the various propagation modes. Fineberg focused on the initiation of frictional sliding and the transition from static to dynamic friction. Three different types of detachment fronts were found experimentally which propagate at very different speeds; in particular, one of the fronts propagated at an intersonic speed. This front led to negligible total slip and negligible change in contact area whereas more slowly propagating fronts led to more significant changes in these quantities. In experiments where sliding initiated under dynamic loading conditions, Ravi-Chandar found that slip pulses could propagate at speeds that were set by the wave that generates slip and not by a characteristic elastic wave speed. Propagation speeds much faster than any characteristic elastic wave speed were found. Rosakis presented experiments that create laboratory earthquakes and, in particular, the propagation speeds of both sides of the rupture front. One side was found to always propagate at the generalized Rayleigh wave speed while the other side could propagate at a sub-shear or super-shear speed depending on conditions. The relation to various analyses were discussed. The propagation speed that occurs is of course dependent on the interface properties. Rice discussed mechanisms of weakening along mature faults and concluded that mature faults are likely to weaken by shear heating and thermal pressurization of pore fluid. These mechanisms are consistent with geological fault studies and with laboratory experiments. Lapusta presented analyses that combined rate and state friction with strong dynamic weakening due to shear heating. Sequences of events were computed to eliminate the influence of initial conditions. Many observed characteristics of earthquake sequences emerged in remarkable detail.

Papers dealing with the effects of fault complexity, branching, and geometric irregularity
include those by Dmowska, Madariaga, Ando, Z. Bazant, and Ohnaka. The relation between
dynamic shear rupture propagation and fault branching was discussed by Dmowska, and Ando.
Dmowska also discussed conditions under which fault branching occurs in a given stress field.
Ando's interest was to investigate how a main fault rupture propagation induces the growth of
secondary branch faults distributed in the main fault zone. Complex fault geometries, including fault kinks, were considered by Madariaga.
He discussed how complex fault geometries influence dynamic shear rupture propagation, and
consequently elastic wave propagation. He also showed in his numerical simulations
that a smooth fault develops supershear rupture propagation, while a more complex (rougher)
fault produces subshear rupture propagation. Ohnaka showed with laboratory experiments
how geometric irregularity of the fault surfaces influences the development of shear
rupture nucleation into dynamic, high speed propagation.
It is widely known that rupture phenomena including earthquakes, are scale-dependent, and
therefore it is important to unravel how scale-dependent shear ruptures can be scaled
rationally in terms of the underlying physics and fault inhomogeneity. The problem of scaling
was dealt with by Z. Bazant and Ohnaka. Z. Bazant discussed size effect on structural fracture
strength from an engineering standpoint, and emphasizes asymptotic properties of the size effect
of cohesive crack model. Ohnaka argued that the process from nucleation to dynamic
propagation scales with the characteristic length defined as the predominant wavelength
contained in the geometric irregularity. He also argued that scale-dependency of scale-dependent
physical quantities inherent in the rupture is ascribed to the scale-dependency of breakdown
displacement, which in turn scales with the characteristic length.

Some experimental, numerical and theoretical studies focused on cases in which the rupture velocity was limited to sub-Rayleigh speeds. Fineberg reported experimentally observed three types of detachment shear waves including a sub-Rayleigh case associated with transitions from static to dynamic propagation. Baumberger presented slip-pulses experimentally observed in gel under shear load; he explained them in terms of the loading condition. On the other hand, Brener presented an alternate theory which introduced a particular friction law between the gel and the surface. Sub-Rayleigh crack-like propagation due to sequential bifurcations of a shear rupture tip was presented by Ando. Marder presented sub-Rayleigh slip-pulses resulting from a material mismatch which arise both in MD simulation and a simple theory. These pulses provide a potentially viable alternative explanation for Coulomb friction.

24 Talks in this area

8/16, 8:30am
Jim Rice (Harvard)
Structure of Mature Faults and Physics of Their Weakening During Earthquakes
8/16, 11:45am
Zdenek Bazant (Northwestern)
Energetic-probabilistic Size Effects in Cohesive Fracture and Asymptotic Matching
8/17, 9:05am
Krishnaswamy Ravi-Chandar (UT Austin)
Experiments on Dynamic Slip
8/17, 10:10am
Eric Dunham (Harvard)
The Dynamics and Ground Motion of Supershear Earthquakes
8/17, 10:45am
Renata Dmowska (Harvard)
Dynamics of Rupture Through Branched and Offset Fault Systems
8/17, 11:20am
Paul Spudich (USGS)
Supershear Rupture Velocity in Recent Earthquakes
8/18, 10:35am
Efim Brener (IFF Juelich)
Fracture and Friction: Stick-Slip Motion
8/19, 8:30am
Michael Marder (UT Austin)
Atoms Matter for Fracture
8/19, 9:30am
Sheldon Wiederhorn (NIST)
Glass Fracture Surfaces Formed at Sub Critical Crack Velocities
8/19, 10:35am
Noam Bernstein (NRL)
Atomistic Simulations of Fracture in Silicon
8/19, 11:10am
Raul Madariaga (ENS)
Earthquake Dynamics from a Seismological Perspective
8/19, 11:45am
Alain Karma (Northeastern)
An Overview of the Phase-Field Approach for Fracture
9/07, 12:00 p.m.
Dr. Loic Vanel (ENS Lyon)
Subcritical Rupture in Heterogenous and/or Plastic Materials: Experiments and Models
9/16, 10:30 a.m.
Dr. Cindy Rountree (Commissariat a l'Energie Atomique)
Molecular Dynamics Simulations of Dynamic Fracture and Plasticity in Amorphous Silica
9/20, 10:30 a.m.
Dr. Nadia Lapusta (Caltech)
Earthquake Models that Account for Dynamic Weakening Mechanisms
9/21, 12:00 p.m.
Dr. Sergio Ciliberto (ENS Lyon)
Failure Time, Critical Behaviour and Activation Processes in Cracks
9/27, 10:30 a.m.
Dr. Elisabeth Bouchaud (Commissariat a l'Energie Atomique)
Damage and Crack Propagation in Silicate Glasses
9/28, 12:00 p.m.
Dr. Daniel Bonamy (Commissariat a l'Energie Atomique)
On the Scaling Properties of Fracture Surfaces
10/06, 10:30 a.m.
Dr. Robert Spatschek (IFF Juelich)
Phase Field Modelling of Fast Crack Propagation
10/06, 3:30 p.m.
Discussion Leader: M. Robbins
Discussion: Disorder
10/25, 10:30 a.m.
Dr. Michael Marder (UT Austin)
Rubber Rupture
11/03, 10:30 a.m.
Drs. Ares Rosakis, Nadia Lapusta (Caltech)
Laboratory Earthquakes: Directionality and Supershear
11/10, 10:30 a.m.
Dr. Miti Ohnaka (Univ Tokyo and UCL)
Rational Constitutive Formulation for Earthquake Ruptures and Physical Scaling of Their Scale-Dependence
11/23, 10:30 a.m.
Dr. Kay Joerg Wiese (Ecole Normale Superieure)
Depinning of Domain Walls, Contact Lines...and Cracks?