This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

The Mechanics of Earthquakes and Faulting

In this paper we propose a new dynamic model for friction. The model captures most of the friction behavior that has been observed experimentally. This includes the Stribeck effect, hysteresis, spring-like characteristics for stiction, and varying break-away force. Properties of the model that are relevant to control design are investigated by analysis and simulation. New control strategies, including a friction observer, are explored, and stability results are presented. >

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A new model for control of systems with friction

The dependence of the friction force on slip history is described by an experimentally motivated constitutive law where the friction force is dependent on slip rate and state variables The state variables are defined macroscopically by evolution equations for their rates of change in terms of their present values and slip rate Experiments may strongly suggest that one state variable is adequate or prove that one is inadequate Analysis of steady slip governed by a single state variable in a spring and (massless) slider predict oscillations at a critical spring stiffness k = kcrit The critical stiffness kcrit is given by a simple formula and steady slip is stable for k > kcrit and unstable for k < kcrit State variable friction laws may superficially appear as a simple slip rate dependence, slip distance dependence, or time dependent static friction, depending on experiment and testing machinery Truly complicated motion is possible in a spring-slider model if more than one state variable is used Further consequences of state variable friction laws can include creep waves and apparent rate independence for some phenomena

Slip instability and state variable friction laws

A survey of models, analysis tools and compensation methods for the control of machines with friction

Passive-dynamic walkers are simple mechanical devices, composed of solid parts connected by joints, that walk stably down a slope. They have no motors or controllers, yet can have remarkably humanlike motions. This suggests that these machines are useful models of human locomotion; however, they cannot walk on level ground. Here we present three robots based on passive-dynamics, with small active power sources substituted for gravity, which can walk on level ground. These robots use less control and less energy than other powered robots, yet walk more naturally, further suggesting the importance of passive-dynamics in human locomotion.

https://science.sciencemag.org/content/sci/307/5712/1082.full.pdf

Efficient bipedal robots based on passive-dynamic walkers.

We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope gamma. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < gamma < 0.015 rad. With increasing gamma, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to gamma 1/3, and that the gravitational power used is proportional to v4 where v is the velocity along the slope.

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The simplest walking model: stability, complexity, and scaling.

Assistant Professor, Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N.Y. 14850 The shear resistance of slipping surfaces at fixed normal stress is given by r = r( v,state). Here V = slip velocity, dependence on «state" is equivalent to functional dependence with fading memory on prior V(t), and ar( v,state) /iJV>O. We establish linear stability conditions for steadY'slipstates (V(t), r(t) constant). For single degree-of-freedom elastic or viscoelastic dynamical systems, instability occurs, if at all, by a flutter mode when the spring stiffness (or appropriate viscoelastic generalization) .reduces to a critical value. Similar conclusions are reached for slipping continua with spatially periodic perturbations along their interface, and in this case the existence of propagating frictional creep waves is established at critical conditions. Increases in inertia of the slipping systems are found to be destabilizing, in that they increase the critical stiffness level requiredfor stability.

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Stability of Steady Frictional Slipping

The authors have built the first three-dimensional, kneed, two-legged, passive-dynamic walking machine. Since the work of Tad McGeer in the late 1980s, the concept of passive dynamics has added insight into animal locomotion and the design of anthropomorphic robots. Various analyses and machines that demonstrate efficient human-like walking have been developed using this strategy. Human-like passive machines, however, have only operated in two dimensions (i.e., within the fore-aft or sagittal plane). Three-dimensional passive walking devices, mostly toys, have not had human-like motions but instead a stiff legged waddle. In the present three-dimensional device, the authors preserve features of McGeer’s two-dimensional models, including mechanical simplicity, human-like knee flexure, and passive gravitational power from descending a shallow slope. They then add specially curved feet, a compliant heel, and mechanically constrained arms to achieve a harmonious and stable gait. The device stands 85 cm tall. I...

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Andy Ruina

Papers

Slip instability and state variable friction laws

Efficient bipedal robots based on passive-dynamic walkers.

The simplest walking model: stability, complexity, and scaling.

Stability of Steady Frictional Slipping

A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees