Dynamics of Rigid Bodies Undergoing Multiple Frictional Contacts

There are several applications in robotics and manufacturing in which nominally rigid objects are subject to multiple frictional contacts with other objects. In most previous work, rigid body models have been used to analyze such systems. There are two fundamental problems with such an approach. Firstly, the use of frictional laws, such as Coulomb\u27s law, introduce inconsistencies and ambiguities when used in conjunction with the principles of rigid body dynamics. Secondly, hypotheses traditionally used to model frictional impacts can lead to solutions which violate principles of energy conservation. In this paper these problems are explained with the help of examples. A new approach to the simulation of mechanical systems with multiple, frictional constraints is proposed which is free of inconsistencies

Spatial and temporal forecasting of large earthquakes in a spring-block model of a fault

We study a recently proposed statistical physics model of earthquake dynamics that includes stress relaxation in the plates as a fundamental ingredient. The model is known to reproduce many realistic features of seismic phenomena, such as: the Gutenberg?Richter law for the event size distribution, the Omori law for aftershocks and an overall velocity-weakening dependence of the average friction force. Here, we analyse the dynamics of the model in detail, in order to investigate to what extent the occurrence of large events in the model can be anticipated. We systematically find that large events occur in fault patches where strain accumulation has exceeded some threshold value. The spatial extent of these patches (which correlate with the magnitude of forthcoming events) can be calculated if the strain state of the system is supposed to be known. In addition, we find that some large events are preceded by well-defined precursor activity. This allows, in a fraction of cases, to complement the forecast of magnitude and spatial location, with a sensible prediction of time of occurrence. Although our work is exclusively limited to the numerical model analysed, we argue that it gives new breath to earthquake forecast techniques that combine the historical analysis of seismic activity with a search of appropriate precursor activity.Fil: Aragón, Luis Enrique. Comision Nacional de Energia Atomica. Centro Atomico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte; ArgentinaFil: Jagla, Eduardo Alberto. Comision Nacional de Energia Atomica. Centro Atomico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte; Argentin

Rate-and-state friction properties of the Longitudinal Valley Fault from kinematic and dynamic modeling of seismic and aseismic slip

The Longitudinal Valley Fault (LVF, Taiwan) is a fast slipping fault (∼5 cm/yr), which exhibits both seismic, and aseismic slip. Geodetic and seismological observations (1992-2010) were used to infer the temporal evolution of fault slip [Thomas et al., 2014a]. This kinematic model is used here to estimate spatial variations of steady-state velocity dependence of fault friction and to develop a simplified fully-dynamic rate-and-state model of the LVF. Based on the postseismic slip, we estimate that the rate-and-state parameter (a – b) σ[over-bar] decreases from ∼1.2 MPa near the surface to near velocity-neutral at 19 km depth. The inferred (a − b) values are consistent with the laboratory measurements on clay-rich fault gouges comparable to the Lichi Mélange, which borders the LVF. The dynamic model that incorporates the obtained (a – b) σ[over-bar] estimates as well as a VW patch with tuned rate-and-state properties produces a sequence of earthquakes with some realistic diversity and a spatio-temporal pattern of seismic and aseismic slip similar to that inferred from the kinematic modeling. The larger events have moment magnitude (M_w∼6.7) similar to the 2003 Chenkung earthquake, with a range of smaller events. The model parameterization allows reproducing partial overlap of seismic and aseismic slip before the earthquake, but cannot reproduce the significant postseismic slip observed in the previously locked patch. We discuss factors that can improve the dynamic model in that regard, including the possibility of temporal variations in (a − b) due to shear heating. Such calibrated dynamic models can be used to reconcile field observations, kinematic analysis, and laboratory experiments, and assess fault behavior

Dynamics of a velocity strengthening fault region: Implications for slow earthquakes and postseismic slip

We consider the effect of permanent stress changes on a velocity strengthening rate-and-state fault, through numerical simulations and analytical results on 1-D, 2-D, and 3-D models. We show that slip transients can be triggered by perturbations of size roughly larger than Lb = Gdc/bσ, where G is the shear modulus, dc and b are the characteristic slip distance and the coefficient of the evolution effect of rate-and-state friction, respectively, and σ is the effective normal stress. Perturbations that increase the Coulomb stress lead to the strongest transients, but creep bursts can also be triggered by perturbations that decrease the Coulomb stress. In the latter case, peak slip velocity is attained long after the perturbation, so that it may be difficult in practice to identify their origin. The evolution of slip in a creep transient shares many features with the nucleation process of a rate-and-state weakening fault: slip initially localizes over a region of size not smaller than Lb and then accelerates transiently and finally expands as a quasi-static propagating crack. The characteristic size Lb implies a constraint on the grid resolution of numerical models, even on strengthening faults, that is more stringent than classical criteria. In the transition zone between the velocity weakening and strengthening regions, the peak slip velocity may be arbitrarily large and may approach seismic slip velocities. Postseismic slip may represent the response of the creeping parts of the fault to a stress perturbation of large scale (comparable to the extent of the main shock rupture) and high amplitude, while slow earthquakes may represent the response of the creeping zones to a more localized stress perturbation. Our results indicate that superficial afterslip, observed at usually seismogenic depths, is governed by a rate-strengthening rheology and is not likely to correspond to stable weakening zones. The predictions of the full rate-and-state framework reduce to a pure velocity strengthening law on a timescale longer than the duration of the acceleration transient, only when the triggering perturbation extends over length scales much larger than Lb

Quasi-dynamic versus fully dynamic simulations of earthquakes and aseismic slip with and without enhanced coseismic weakening

Physics-based numerical simulations of earthquakes and slow slip, coupled with field observations and laboratory experiments, can, in principle, be used to determine fault properties and potential fault behaviors. Because of the computational cost of simulating inertial wave-mediated effects, their representation is often simplified. The quasi-dynamic (QD) approach approximately accounts for inertial effects through a radiation damping term. We compare QD and fully dynamic (FD) simulations by exploring the long-term behavior of rate-and-state fault models with and without additional weakening during seismic slip. The models incorporate a velocity-strengthening (VS) patch in a velocity-weakening (VW) zone, to consider rupture interaction with a slip-inhibiting heterogeneity. Without additional weakening, the QD and FD approaches generate qualitatively similar slip patterns with quantitative differences, such as slower slip velocities and rupture speeds during earthquakes and more propensity for rupture arrest at the VS patch in the QD cases. Simulations with additional coseismic weakening produce qualitatively different patterns of earthquakes, with near-periodic pulse-like events in the FD simulations and much larger crack-like events accompanied by smaller events in the QD simulations. This is because the FD simulations with additional weakening allow earthquake rupture to propagate at a much lower level of prestress than the QD simulations. The resulting much larger ruptures in the QD simulations are more likely to propagate through the VS patch, unlike for the cases with no additional weakening. Overall, the QD approach should be used with caution, as the QD simulation results could drastically differ from the true response of the physical model considered