Here I summarize several research projects that have occupied my energies over many years. I hope that you might find them useful, instructional, or at least moderately interesting. For that reason, I present them as case-study narratives. These are examples of the stories behind research, and are not scientific papers. I intend these to be short summaries, but it is easy to carry on for too long.
In general, these projects involve the application and development of methods in experimental mechanics to solve problems in geomechanics, biomechanics, design, and so on. For instructional reasons, I include narratives about the nature of each problem that led to choice of technique. Some mistakes and silly decisions are apparent in retrospect. Some of the results and findings are summarized.
It will take me awhile to complete this page, so it is a work in progress. My intent is to eventually include some representative photographs from each project. In the meantime, should you be so inclined, you can track down details about these projects by starting with my book and the related papers in my publication list.
Your patience is appreciated.
Some results and conclusions:
1. Resistance strain gage rosettes can be used to measure the strains as a function of time in glaciers and similar natural surfaces.
2. This method is somewhat tedious and only point-wise data are obtained, but sensitivity, range, and accuracy are appropriate to the problem, and standard equipment is readily available.
3. It is not necessary to use posts in the ice to attach the strain gage wires to. With proper care, they will freeze into the ice.
4. The strain rates in maritime glaciers appear to be affected by the weather, particularly the rainfall.
5. Results suggested, but did not prove conclusively that glacier flow is affected by the moon: that is, glaciers exhibit tides.
6. White-light speckle photography and optical data processing provide a way to obtain deformation data for large areas (ca. 10 kilometers square) of a glacier in a short time.
7. Glacier flow rates are such that two speckle photographs taken 24 hours apart will give the correct sensitivity.
8. A stereo-pair set of speckle photographs is needed in order to map flow rates from the photographs back to the surface in this three-dimensional situation.
9. Surface flow rates of maritime glaciers is affected by weather, particularly rainfall and the resulting overburden of saturated ice.
10. It appears that maritime glaciers exhibit tides; that is, the flow rates are affected by the moon.
11. Terrestial atmospheric turbidity affects resolution limit if the speckle photographs, thereby limiting sensitivity.
12. The limitations imposed by terrestial atmospheric turbidity can be understood and explained using a variation of the approach used in astronomy.
In 1970, shortly after returning from Zambia, I was invited to lecture on mechanics of deformable solids and related topics for the Foundation for Glacier Research (FGR) and the Juneau Icefield Research Program (JIRP). These programs were originated and developed into thriving glaciological research and training arenas by the emminent glaciologist, Dr. Maynard Miller, then a professor at Michigan State University.
Prior to that first season, I became aware of the interest in understanding the mechanics of glaciers. I was surprised that relatively little was known about the surface strain rates, let alone the deep-ice flow and strain rates of these rivers of ice. Further, I discovered that the glaciologists relied on surveying techniques to gather the needed data. The difficulties are readily apparent, and include: (1) the problem is poorly conditioned in that the flow data requires determination of the small difference between large quantities, thereby creating serious problems with the propagation of uncertainty; (2) given the possible errors in flow data, the errors and scatter in strain rate data, basically the derivative of the flow rate, would be large; (3) because of lack of sensitivity, the survey data had to be taken over a long period of time (weeks, full season), meaning the measuring locations had moved down-glacier betweeen the beginning and end of observations; (4) relatively small areas of the glacier could be studied. It seemed that better methods had to be found in order to obtain data that would facilitate quantitative understanding of glacier mechanics.
Methods and experiences:
1. Microwave interferometry
The sensitivity and range criteria suggestd the use of microwave interferometry. Laboratory experiments suggested that the method would work, although there were serious concerns about the lack of truly rugged microwave signal generator, detector, and antennae. With the help of strong backs owned by several program participants, we trundled a large case of microwave devices to the Vaughan-Lewis glacier in the Juneau icefield. Weather was terrible, but we got the experiment set up. One data point was collected before the power supply in the microwave power meter failed owing to spikes in the generator output. That finished the experiment.
2. Resistance strain gages
At this point, doctoral student Gordon Warner took an interest in this problem for his dissertation project. We discussed several potential approaches, and it seemed that electrical resistance strain gages and strain rosettes offered the best solution. The idea was to embed posts into the ice and make relatively large single wire strain gages by stretching wires between the posts. The wires would actually be embedded in channels in the ice with the hope that they would freeze in place, although this was problematical because of the thermal dynamics of maritime glaciers. Gordon devised 10-meter gages and calibrated them. An ordinary battery-powered strain indicator was used. While at it, we decided to set up two three-element strain rosettes so as to be able to obtain principal strains and angles. The equipment was taken to the Ptarmigan glacier above Juneau and installed. It worked very well, and strain data were obtained over a period of about 10 days before the setup ablated out.
Given success with the pilot experiment, the technology was refined, particularly with regard to weatherproofing the setup and the instruments, and a more elaborate experiment was carried out the next year. Excellent results were obtained early on, so we wrapped in all up and I want fishing. These data formed the basis of Gordon's dissertation.
Sensitivity and range were correct, and the required data are obtained over a relatively short time. But, two problems with this approach are apparent: (1) it is still point-by-point, (2) it is tedious, especially without telemetering and automatic recording. We were packing the strain indicator a mile or so down to the measurement site every few hours, all weather, day and night.
3. White-light speckle photography
I had been considering using a moire method that employed grating photography and optical Fourier processing that I had developed for a laboratory-scale project in the area of fastening. The grating could be created in the snow-covered part of the surface of a glacier by carefully driving a snow vehicle across it. About that time, I had also been working with white-light (noncoherent-light) speckle photography as a means of getting strain data from large buildings, human skin and flowing fluids. A glacier surface is actually quite rough over a span of length scales. It seemed that it should be possible to photograph the surface under low-angle sunlight so that the shadows of the small-scale asperities would create a speckle pattern. If this could be accomplished on successive days, so as to make a double-exposed speckle photogaph, then the local surface motions could be obtained using Young's fringes of optical Fourier processing, as we were doing for other problems. Clearly, high-resolution photography with fine-grain, high contrast film (meaning holographic plate) would be required.
Graduate student Edgar Conley decided to pursue this idea for his doctoral dissertation, and undergrad research assistant Eric Burgoon also was intrigued by the project and the potential field experience.
To test the approach, a high-quality view camera was ruggedized and taken by the students to Nisqually glacier on Mount Rainier. It was set up on the valley wall overlooking the upper glacier, and two exposures taken on successive days (two sunny mornings in a row--unusual). The plate was taken to the motel room and devloped in the sink, then interrogated with the beam of the laser that was taken along. Young's fringes were visible immediately. This was one of those rare times when an experiment works well the first time. Several more double-exposure plates were made, and the experiment was terminated earlier than planned because the results were beyond expectations. The main problems were tourists and bears messing with the camera overnight.
The data were analyzed back in the lab, and it became clear that a stereo pair of pictures were required in order to map the deformations from the photoplate back onto the glacier surface.
Two special-purpose cameras were built using surplus aerophotography lenses, schedule-80 pipe, and rugged plate holders. During the final season, experiments were carried out at Nisqually and Ptarmigan glaciers with postive results. A problem that had to be looked into and solved was the effect of terrestial atmospheric turbidity on the resolution limits of optical images. This had been studied by astronomers, but data on the terrestial problem were meager. A variation of the astronomical approach was devised and proven by Dr. Conley.
Much of this work was supported by the National Science Foundation.
Some results and conclusions:
Methods and experiences:
An ideal method for using moire for out-of-plane differential displacement measurement or contour mapping involves projecting the reference grating on the specimen by means of, for example, a slide projector. The analysis is quite similar to that of shadow moire, which has been used for absolute contouring in biomechanics, particularly for the diagnosis of scoliosis. One distinct advantage of projection moire is that only a small transparency of the reference grating is required. Shadow moire, on the other hand, requires a master grating that is as large as the object being studied. Another advantage is that, if the surface is not initially flat, its out-of-plane displacement may be determined from only one double-exposure photograph. With shadow moire, one would need to calculate the difference in contours given by two separate fringe photographs, which is a poorly conditioned problem in terms of potential error propagation. In fact, the difference between contours of two entirely distinct objects is easily determined by projection moire.
Here is the general idea. Suppose that an image of a line grating is projected into the specimen space, and the image is simply photographed for different specimens. The grating image will appear distorted by the out-of-plane projections of the object. Exposure one is recorded with the first object, and then the second object is put into its place for the second exposure. The moire fringes indicate the contour difference between the two objects. If the first object is a flat surface, then the fringes are a normal contour map of the object. Otherwise the mismatch between the objects is established.
Application of this technique in the area of biomechanical contouring was pursued by Dr. Paul Moga, D.O., who was working on a second degree in biomechanics.
The procedure was quite simple and seems adequately described by the two figures below. The first figure is an isometric schematic of the experimental arrangement used in the biomechanical studies under discussion. The second illustration is a sample of one of the moire fringe patterns obtained by double exposure between the at-rest state and a specified degree of muscle contraction effort expressed as a fraction of the subject's maximum voluntary contraction. Such fringe patterns were recorded for several different levels of muscular effort in various subjects. They were analyzed to obtain plots of out-of-plane displacement as a function of percent of maximum voluntary contraction.
Figures to be provided soon!
Some results and conclusions:
Note: Results of this research were voluminous, and only a summary of general observations, mostly related to methodology, are given here.
Methods and Experiences:
Moire with optical processing:
An extension of geometric moire that was developed by Cloud for investigations of the strain fields near coldworked fastener holes seemed to be appropriate for the 3-D fracture problem. The method utilizes direct photography of the specimen gratings for whatever specimen states are of interest. The grating photographs are superimposed with one another or with submaster gratings in an optical spatial filtering system to form moire patterns.
There are several attractive aspects of the moire technique which incorporates spatial filtering. The fundamental idea is to take advantage of the sensitivity multiplication and noise reduction offered by optical Fourier processing of moire grating photographs which are recorded for various states of a specimen. Sensitivity of the method can be controlled after the experimental data are recorded, within limits which are between those of geometric and interferometric moire. The method also is very flexible in that any two specimen states can be compared easily. The original data are permanently recorded for leisurely study later. Certain common errors are automatically eliminated. Fringe visibility is usually much improved over what is obtained by any method of direct or optical superimposition. Finally, the method is useful in difficult environments. An important characteristic of this procedure is that it operates in a differential mode, which, as a rule, is best in any experiment.
A multiple embedded grid adaptation of this enhanced moire method was developed to study the strain on the surfaces, quarterplanes, and midplane of thick specimens made of polycarbonate. Most of this work was accomplished by doctoral student Somnuek Paleebut. The grids on the surface and in the interior are recorded for the unloaded condition and for various loaded states using high-resolution photographic techniques. The interior gratings are photographed through the out-of-focus intervening gratings. Moire fringes are extracted using optical Fourier processing. An empirically-based correction procedure to eliminate the errors caused by the material refraction effect has been derived. The need for such a correction for errors caused by gradients of refractive index is not unique to embedded grid moire. The developed approach could be used to reduce errors when other optical methods, such as speckle, moire interferometry, or holointerferometry are used to measure strain or deformation in the interior of solids.
Support: National Science Foundation