Neutral elastic deformations
Elastic bodies or systems may not require external energy for certain finite and continuous deformations. Conditions providing these kinds of effortless, or neutral, deformations are discussed.
Durum, M. M.↗
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A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems
Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.
Avis, L. M.↗
Simplified solution for elliptical-contact deformation between two elastic solids
A linear regression by the method of least squares is made on the geometric variables that occur in the equation for elliptical-contact deformation. The ellipticity and the complete elliptic integrals of the first and second kind are expressed as a function of the x,y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). The procedure for solving these variables without the use of charts or a high-speed computer would be quite tedious. These simplified equations enable one to calculate easily the elliptical-contact deformation to within 3 percent accuracy without resorting to charts or numerical methods.
Brewe, D. E.↗
Influence of adsorbed fluids on the rolling contact deformation of MgO single crystals
Basic phenomena associated with rolling contact deformation were studied using MgO as a model bearing material. A hardened steel ball was rolled on MgO single crystals in slow-speed reciprocating motion and in high-speed circular motion. The resulting deformation was studied by dislocation etch-pit techniques. The presence of adsorbed fluids, such as silicone oil, white mineral oil, and toluene, with slow-speed sliding caused a dramatic change in slip mode and premature surface spalling compared with similar experiments in air or under water. In contrast, dimethyl formamide inhibited these slip processes. The results are consistent with the dependence of dislocation mobility on adsorbed species. High-speed hydrodynamic rolling with mineral oil lubrication produced a different slip phenomena entirely from the slow-speed rolling. The slip bands resembled those produced in tensile tests, and all slip apparently initiated at subsurface sites.
Dufrane, K. F.↗
Precursors to failure in rocks while undergoing anelastic deformations
Specimens of pyrophyllite, which exhibits large anelastic deformation before brittle failure, were stressed to failure in a biaxial press to model stress accumulation prior to an earthquake. Optical holography, sound velocity measurements and photography through transparent pistons were used to study the specimens. A zone of preferential deformation around the incipient fault was monitored at 50% or more of ultimate failure strength; reversals of seismic velocities and formation of en echelon cracks near the coming macrocrack were also observed. The dependence of the seismic velocity reversals on moisture was noted.
Sobolev, G.↗
Deformation at the Decaturville impact structure, Missouri
The Decaturville structure is a small area of intense disturbance marked by surface exposure of Precambrian rock and minor lead-zinc mineralization. The present paper gives a detailed analysis of the associated deformation processes on the basis of detailed mapping and study of drill core. The presence of shock-deformation features and the complex structural pattern revealed from the analysis are strong indications that the Decaturville structure was formed by impact of an extraterrestrial body.
Offield, T. W.↗
Implications of very long baseline interferometry measurements on North American intra-plate crustal deformation
Very Long Baseline Interferometry experiments over the last 1-3/4 years between Owens Valley, CA and Haystack, MA Radio Observatories suggest an upper limit of east-west crustal deformation between the two sites of about 1 cm/yr. In view of the fact that the baseline between the two sites traverses most of the major geological provinces of the United States, this low rate of crustal deformation has direct relevance to intra-plate crustal tectonics. The most active region traversed by this baseline is the Basin and Range province, which was estimated by various researchers to be expanding in an east-west direction at rates of .3 to 1.5 cm/yr. The Colorado Plateau and Rocky Mountain system also appear to be expanding, but at a somewhat lower rate, while east of the Rocky Mountains, the predominant stress appears to be compressional, nearly horizontal, and east to northeast trending.
Allenby, R. J.↗
Anisotropic friction, deformation, and fracture of single-crystal silicon carbide at room temperature
Anisotropic friction, deformation, and fracture studies were conducted with /0001/, /10(-1)0/, and /11(-2)0/ silicon carbide surfaces in sliding contact with diamond. The experiments were conducted with loads of 0.1, 0.2, and 0.3 N at a sliding velocity of 3 mm/min in mineral oil or in dry argon at room temperature. The 1010 direction on the basal /0001/ plane exhibits the lowest coefficient of friction and the greatest resistance to abrasion for silicon carbide. Anisotropic friction and deformation of the /0001/, /10(-1)0/, and /11(-2)0/ silicon carbide surfaces are primarily controlled by the slip system /10(-1)0/ 11(-2)0. The anisotropic fracture during sliding on the basal plane is due to surface cracking along /10(-1)0/ and subsurface cracking along /0001/. The fracture during sliding on the /11(-2)0/ or /10(-1)0/ surfaces is due to surface cracking along /0001/ and /11(-2)0/ or /10(-1)-1 and to subsurface cracking along /10(-1)0/.
Miyoshi, K.↗
Regional deformation of mare surfaces
The possible tectonic significance of large topographic irregularities within Mare Serenitatis is discussed, and the characteristics of sinuous rilles are considered as possible indicators of structural deformation. It is shown that most sinuous rilles have been structurally warped and that their slopes lie within the laminar flow range. The sinuous rilles may have been formed in the domain of turbulent flow, if the ratios of meander wavelength to channel width can be taken as indicators. Some surface tectonic deformation occurring before the broad uplift of the basin center is suggested by the surface topography and radar reflectors in the Mare Serenitatis.
Scott, D. H.↗
Origin of multi-ring basin ridge systems - An upper limit to elastic deformation based on a finite-element model
A finite-element model of a 500-km diameter lunar basin flooded with 10 km of basalt was used to represent the central portion of a multi-ring basin undergoing elastic deformation as a result of basin subsidence. Gravitational forces due to the weight of the basalt were set as the initial forces in the model; elastic constants computed from seismic velocities of lunar samples provided strength specifications. In addition, the crust was constrained by permitting no displacements at a depth of 60 km. Because of the strength of the lithosphere, surface subsidence amounted to only 20 m. This magnitude of elastic deformation does not equal that found on the lunar surface, but the orientation of principal stress and the position of circumferential compressional stress are compatible with the evolution of inner-ring and radial ridge systems by gravitational-induced downdropping.
Maxwell, T. A.↗
Radial deformation of the solar current sheet as a cause of geomagnetic storms
It is suggested that the solar current sheet, extending from a coronal streamer, develops a large-scale radial deformation, at times with a very steep gradient at the earth's distance. The associated magnetic field lines (namely, the interplanetary magnetic field (IMF) lines) are expected to have also a large gradient in the vicinity of the current sheet. It is also suggested that some of the major geomagnetic storms occur when the earth is located in the region where IMF field lines have a large dip angle with respect to the ecliptic plane for an extended period (6-48 h), as a result of a steep radial deformation of the current sheet.
Akasofu, S.-I.↗
System for near real-time crustal deformation monitoring
A system is described for use in detecting earth crustal deformation using an RF interferometer technique for such purposes as earthquake predictive research and eventual operational predictions. A lunar based RF transmission or transmissions from earth orbiting satellites are received at two locations on Earth, and a precise time dependent phase measurement is made of the RF signal as received at the two locations to determine two or three spatial parameters of the antenna relative positions. The received data are precisely time tagged and land-line routed to a central station for real-time phase comparison and analysis. By monitoring the antenna relative positions over an extended period of months or years, crustal deformation of the Earth can be detected.
Macdoran, P. F.↗
Stresses and deformations in elliptical contacts
Topics presented deal with defining conformal and nonconformal surfaces, curvature sum and difference, and surface and subsurface stresses in elliptical contacts. Load-deflection relationships for nonconformal contacts are developed. The deformation within the contact is, among other things, a function of the ellipticity parameter and elliptic integrals of the first and second kinds. Simplified expressions that allow quick calculations of the deformation to be made simply from a knowledge of the applied load, the material properties, and the geometry of the contacting elements are presented.
Hamrock, B. J.↗
Crustal deformation at very long baseline interferometry sites due to seasonal air-mass and ground water variations
The seasonal deformation normal to the Earth's surface was calculated at stations involved or interested in very long baseline interferometry (VLBI) geodesy and at hypothetical sites in Australia and Brazil using global atmospheric pressure data, values for groundwater storage, and load Love numbers deduced from current Earth models. It was found that the annual range of deformation approached the centimeter level measuring potential of the VLBI technqiue at Greenbank, Haystack, and the Brazil site.
Stolz, A.↗
Some possible effects of solid-state deformation on the thermal evolution of ice-silicate planetary bodies
Several ways in which solid-state deformation could be important in the evolution of an ice-silicate body are considered. The considerations suggest several scenarios for the evolution of Ganymede and Callisto which might be tested on the basis of Voyager and Galileo results. Several potential sources of heat may have caused extensive melting early in the history of these bodies, including a high initial luminosity of Jupiter, accretional heating, gravitational segregation of ice and silicates in a homogeneously accreted body, and deformation by synchronous rotation. The analysis leads to the conclusion that two mechanisms - diapirism and solid-state convection - could be sufficient to inhibit the development of an excessive liquid water mantle, or to cause refreezing of such a mantle formed prior to steady-state conditions or from other heat sources.
Parmentier, E. M.↗
Time dependent deformation and stress in the lithosphere
Efficient computer programs incorporating frontal solution and time stepping procedure were developed for the modelling of geodynamic problems. This scheme allows for investigating the quasi static phenomena including the effects of the rheological structure of a tectonically active region. From three dimensional models of strike slip earthquakes, it was found that lateral variation of viscosity affects the characteristics of surface deformations. The vertical deformation is especially informative about the viscosity structure in a strike slip fault zone. A three dimensional viscoelastic model of a thrust earthquake indicated that the transient disturbance on plate velocity due to a great plate boundary earthquake is significant at intermediate distances, but becomes barely measurable 1000 km away from the source.
Yang, M.↗
Occurrence of cohesion of metals during combined plastic deformation
Experiments were conducted to study the cohesion of metals with surface films of varying thickness and hardness. It was established that the deformation necessary for the occurrence of cohesion is determined by the correlation of mechanical properties of the films and the base metal. The greater the relative hardness of the film the lower the deformation necessary for the occurrence of cohesion. The films are as plastic as the base metal prevent cohesion, since in this case it is impossible for sections of metal to appear that are free of contaminants. The physical perculiarities of metals that determine their capability for coalescence under conditions of dry friction are the relative hardness and plasticity of the oxide films formed on their surface under atmospheric conditions.
Aynbinder, S. G.↗
The influence of a local wall deformation on the development of natural instabilities in a laminar boundary layer
The natural instabilities which propagate in the laminar boundary layer of a flat plate composed of intermittent wave trains are described. A spectral analysis determines the frequency range and gives a frequency and the harmonic 2 only if there is a wall deformation. This analysis provides the amplitude modulation spectrum of the instabilities. Plots of the evolution of power spectral density are compared with the numerical results obtained from the resolve of the Orr-Sommerfeld equation, while the harmonic is related to a micro-recirculating flow near the wall deformation.
Burnel, S.↗