PHYSICAL MATHEMATICS SEMINAR
TOPIC: Elastodynamic analysis of frictional sliding
SPEAKER Nadia Lapusta
Postdoctoral Fellow
Division of Engineering and Applied Sciences
Harvard University
ABSTRACT:
Consider two identical elastic solids pressed together by constant normal
stress and slowly loaded so as to make them slide on the resulting planar
interface. Despite the simplicity of the problem's geometry, the patterns
of spontaneous slip accumulation can be very complex due to the interplay
of frictional properties of the interface and inertial effects in the
surrounding solids. Possible outcomes include continuous creep, sequences
of episodes of rapid slip, and their combination in space and/or in time.
In addition, each rapid episode incorporates complexities of its own, such
as quasi-static nucleation of slip on a part of the interface followed by
dynamic expansion of the slipping zone, often with non-trivial features
such as self-healing slip pulses.
To describe frictional properties, we employ non-linear rate and state
friction laws which are experimentally derived and incorporate the current
"state-of-the-art" understanding of macroscopic frictional response. I
will present linearized stability analysis and other considerations
showing that these laws, and not simpler classical descriptions, provide
frictional sliding with mathematically and physically meaningful stability
properties and describe the full range of slip behavior.
This setting can serve as a basis for simplified models of faults in the
Earth's crust, with rapid slip corresponding to the occurrence of
earthquakes. By simulating spontaneous slip accumulation in these models,
we study qualitative features of earthquake sequences and individual
earthquakes. Such simulations are very challenging because of the variety
of temporal and spatial scales involved. To make the simulations
tractable, we have developed an efficient numerical algorithm. I will
discuss the main ideas of the algorithm and some simulation results.
DATE: Tuesday, February 19, 2002
TIME: 2:30 PM
LOCATION: Building 2, Room 338
Refreshments will be served following the seminar in Room 2-349.
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139