Applied Mathematics Seminar
Monday, April 27, 1998, 4:00pm, 120 Physics
Brian Hayes (Duke University, Dept of Math)
Stress-Controlled and Velocity-Controlled Shear Waves in a Saturated Granular Medium

Abstract:

We study the interaction of plane shear waves, when either the stress or velocity is a given periodic function on the boundary. The soil is modelled as a continuum, obeying a hypoplastic flow rule. In both cases, wave interactions are confined to a strip of width $x_I$, along the boundary. As $t\to\infty,$ $x>x_I,$ the velocity and stress approach asymptotic, time-independent values. For the stress-controlled case, the saturated state depends smoothly on the boundary data and is independent of the initial data. In the velocity-controlled case, however, the asymptotic state exhibits a wildly discontinuous, fractal behavior, as the boundary data is varied. (joint work with Dave Schaeffer)

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