Two-dimensional Elastic Medium Research Articles

Equivalent crack formation by propagating cracks under tension

A hybridized displacement discontinuity element and indirect boundary element (or fictitious stress) procedure is being used to model crack propagation in cases involving one, two and three cracks in a two-dimensional linear elastic medium under tension or partial tension/ compression. By comparing with published results, the simulation results are found to be satisfactory and the hybridized procedure (called FROCK) is verified. It is interesting to discover that in each of the cases involving one, two and three cracks, an equivalent crack perpendicular to the direction of maximum tension is formed through propagation of the outer and inner crack tips. An important capability of FROCK is shown in a complicated case with applied compression and tension in which parts of the crack and crack extensions open up while the rest remain closed with shear resistance acting on the closed crack surfaces.

Stress distribution for a rigid fractal embedded in a two-dimensional elastic medium.

Stress distribution for a rigid fractal embedded in a two-dimensional elastic medium.

Finite difference calculations of dispersive Rayleigh wave propagation

This paper describes the method and results of the numerical modeling of Rayleigh wave propagation in media with velocity variations in both vertical and horizontal directions. The P-SV equations of motion in a general two-dimensional Cartesian elastic medium are approximated as second order finite difference equations. A second order free-surface condition is required to produce a noise-free solution. A band-limited pulse composed solely of the Rayleigh wave eigenfunctions for a uniformly layered medium is the initial condition. Numerical experiments simulating propagation in a plane layered structure allow greater accuracy in two station determination of Rayleigh wave phase velocities than that obtained in the field. In a medium with laterally varying velocities the numerical experiments include the local conversion of Rayleigh waves to higher modes and body waves and therefore model the contamination of phase velocity measurements by converted waves. As such, the numerical experiments simulate the seismic experiment conducted over a laterally varying structure under the restrictions that the structure is approximately two-dimensional and the illuminating wavefield crosses the structure perpendicularly to the structural strike. A sloping layer separating two waveguides of different thicknesses produced a minor directional dependence in Rayleigh wave phase velocities measured from updip and downdip traveling waves. The directional dependence is usually less than half that observed in numerical experiments of Love wave propagation in a similar structure. Analysis of several other simple structures leads to three conclusions. First, Rayleigh wave phase velocities measured over a region of lateral velocity variation exhibit small directional dependence unless the transition is very abrupt. Second, the dispersion measured across a laterally varying structure falls within or nearly within the bounds of the dispersion of the extreme plane layered structures derivable from the transition zone structure. Third, the numerical experiments indicate that the phase velocities measured across a slowly varying structure reflect the properties of the structure beneath the array.

Comparison of the effects between single and multiple scattering on coda waves for local earthquakes

The effects of multiple scattering on coda waves have been investigated by an extension of the single-scattering theory. The contributions to the coda power due to multiple scattering from a uniform distribution of isotropic scatterers in a two-dimensional infinite elastic medium have been numerically evaluated. The results show that at shorter lapse time, the coda power is well explained by the single-scattering theory. At longer lapse time, the effects of multiple scattering need to be considered. The neglect of multiple scattering gives rise to an overestimation of the values of the quality factor ( Q ) by a factor of 1.4.

Specific heat of adsorbed films of3He,4He, and isotopic helium mixtures near monolayer coverages

Specific heat results are presented for near-monolayer films of3He,4He, and isotopic He mixtures adsorbed on Vycor porous glass in the temperature range between 1 and 4°K. In the case of the pure He monolayers and submonolayers, the specific heats depend only onT 2 , like a two-dimensional Debye elastic medium. A film of slightly greater than monolayer coverage needs an additional temperature-independent term. Monolayer coverages of mixtures are difficult to define, but all coverages used, some of which are submonolayer, need bothT 2 andT-independent terms. The constant term may arise from atoms in the second layer forming a classical noninteracting system, which in the mixture case would indicate selective adsorption of4He in preference to3He at the substrate wall, in agreement with previous adsorption experiments on the same substrate.