Friday, March 03, 2006

2003 Timoshenko Medal Lecture by Ben Freund

Reflections and Refractions

L. B. Freund, November 19, 2003


Friends and colleagues, I've attended many Applied Mechanics Dinners over the years, but this one has been the most enjoyable so far. Hopefully, that view will survive the next 20 minutes or so.

It's a singular honor to receive the Timoshenko Medal of ASME. For one thing, it's deeply gratifying to get a pat on the back from one's peers. It's also a privilege to have one's name added to the list of previous recipients, which includes so many individuals for whom I have the deepest respect.

Stephen Timoshenko himself had withdrawn into retirement long before I discovered that I had an interest in his field, and I never encountered him in person. However, I do have something of a direct connection to Timoshenko, in that he is my academic great great great grandfather. The appearance of his advanced textbooks on mechanics was surely among the defining events for the field in the 20th century.

A few months ago, long before I had given any thought to this evening's remarks, I was asked to provide a title. It seemed safe enough to adopt the tone of Timoshenko's memoirs by choosing Reflections and Refractions, borrowing a couple of terms from wave propagation. The intention of the term Reflections in this context is self-evident. The term Refractions was added as a reminder, mainly to myself, that recollections can possibly become distorted when viewed through the medium of elapsed time. In any case, I intend to follow tradition by reflecting on aspects of my own experiences in the field, hopefully with no more refraction than my years will allow.

My pioneer ancestors had the foresight to settle in a place that would eventually establish a superb state university. I might mention that, when John Hutchinson first learned some years ago that I had been raised on a farm in rural Illinois, he suggested that perhaps I had overcompensated for it. Eventually, I enrolled at the University of Illinois to study electrical engineering. Inspired by a course on dynamics that was then required for electrical engineering, I changed my major to engineering mechanics at the end of my second year, whereupon Chuck Taylor became my academic adviser.
Throughout my undergraduate years, I worked all summers and holidays for a company that manufactured earthmoving equipment and airport towing tractors. My job was involved with field testing these machines, including for example the first towing tractor designed specifically for the Boeing 747, then on the drawing board. With an eye toward a more interesting job than I saw being done by engineers at this company, I continued on for a master's degree at Illinois. It was during this time that talented people such as Henry Langhaar and Marv Stippes opened my eyes to the rewards of an in-depth understanding of this stunningly beautiful subject we all deal with. To pursue that ideal for myself, it was off to Northwestern to continue graduate study.

Upon arrival in Evanston, Jan Achenbach became my research adviser, another of my many good fortunes. He proposed interesting topics for us to study, and he gave me the chance to work with a good deal of independence. This approach invariably leads to rewarding surprises in the learning process and it allows one to benefit even from mistakes or from false starts, of which there were plenty, and I've tried to follow the same approach with my own research students and postdocs. The knowledge gained in doing a thesis on diffraction of elastic waves turned out to be invaluable within just a few years. Of most significance, I think, was an appreciation of the awesome power of some fundamental theorems in analytic function theory that underlie the operational techniques in applied mathematics that we usually take for granted.

After Northwestern, it was off to Brown for a one-year post-doctoral fellowship. At a birthday symposium earlier this year, Jan Achenbach recalled thinking at the time that this was going to be another case of a promising young person being lost to plasticity. I did try my hand at plasticity but also found other interesting things to do. Eventually, I joined the regular faculty at Brown, and one year became many years.

In the early days, my usual path to the coffee room in the morning took me past Jim Rice's office on the seventh floor of our building. On a particular morning in 1970, he showed me a reprint that he had just received in the mail from Jock Eshelby. This paper dealt with dynamic mode III crack growth at nonuniform rates. To someone with experience in wave propagation, the results reported in the paper, particularly the appearance of sharp discontinuities on wavefronts in two dimensions, were astonishing. We wondered if it was possible that the same remarkable physical features could also arise in the more realistic case of tensile cracking. At the time, it seemed unlikely because of the existence of surface waves in the latter case.

Neither books nor courses on fracture mechanics yet existed, and I knew absolutely nothing about stress intensity factors or energy release rates. Nonetheless, the appeal of a new area trumped my ignorance of the lore of the subject, and I adopted this problem in crack dynamics as something of a mission. During the next year, there was no progress whatsoever concerning accelerating tensile cracks, although I did learn other things about crack dynamics. Finally, one afternoon while working alone at the blackboard in my office, the fog lifted and things came together; I can still picture in my mind the diagrams that were on the board.

The work was completed within the next few months and the key papers were submitted for publication. To this day, I remain indebted to my senior colleagues at Brown for having provided an atmosphere in which an assistant professor could devote a couple of years to a substantial project in this way, and have striven to provide a similar environment for other young people as they've come along. As an aside, I also came to know Eshelby a few years later, when he coupled a trip to the U.S. to receive his Timoshenko Medal with an extended stay with our group at Brown, which was a fascinating and entertaining few weeks for us.

A particular dynamic fracture phenomenon of interest in those days was the type of shear cracking that occurs in earthquakes. At about this time, seismologists were concluding that the dislocation based models that they had been using to describe faulting in the crust of the Earth were overly constrained. They were now looking for fully kinetic models in which neither driving force nor kinematic response was specified a priori. These shear crack models provided an ideal starting point for addressing the issue. This connection provided an opportunity for me to work for a number of years in a field quite different from my own. The people I came to know -- seismologists and geophysicists - are a very talented group and it was a great pleasure to be included as an adopted member of that community for some years. The special focus they have on this one thing -- the earth -- took some getting used to. They are not inclined to think about ways to improve it, a natural tendency for engineering.

Another interesting set of issues for which dynamic fracture mechanics played a central role concerned structural safety and reliability. Perhaps the main issue of the day was arrest of running fractures in tough structural materials, reactor pressure vessels or ship hulls for example, accepting that crack initiation was inevitable. There was good progress on plasticity effects in dynamic fracture during this period in the course of productive collaborations with my students and postdoc, as well as with John Hutchinson and his students.

A related problem in which I became involved, initially on a consulting basis, was explosive rupture of long sections of natural gas transmission lines. Conventional wisdom held that the problem would vanish if one used pipeline steels that retained their ductility at high deformation rates. The reasoning was that, during rupture of a pressurized pipeline, the pressure release wave generated by escaping gas would always outrun a ductile crack and pipeline damage would be localized. However, nature doesn't always conform to conventional wisdom. Accidents in which miles of operating pipeline were ruptured explosively continued to occur. To try to understand how this could be so, a consortium of pipeline producing companies ran a series of dramatic full-scale tests on instrumented pipelines that confirmed field experience, and they wanted some assistance in interpreting the observations.

I mention this project mainly because it's an example of an important mechanics problem that is incredibly messy, involving large deformation, plastic flow, ductile fracture, inertial forces, gas dynamics, and possibly soil mechanics, one of the most mysterious of the practical arts. There are few clues on how to proceed with sorting it out. However, by means of some calculations based on overall power balance, done in collaboration with Dave Parks and Jim Rice, we were able to pin down the reason for the sustained long running ductile fractures and to identify strategies for implementing mechanical crack arresters. While such problems are rarely discussed in books or in the classroom, they represent some of the most pressing issues in our line of work. A key step to progress, it seems to me, is in identifying the appropriate level of detail for approaching the problem. The most refined level is not always the most appropriate. Perhaps this particular problem seems dated in the micro-nano era, but I believe that the point of view is scale invariant.

Some time in the mid 1980s, two small things happened that would have long-term ramifications for me. First, Cambridge University Press asked about my interest in writing a monograph on dynamic fracture. The preparation of such a book is a time-consuming and sometimes tedious task, as many of you know. However, the subject itself had developed in a sporadic way, typical of basic research. Writing a book offered the prospect of describing the whole journey through the subject as a continuous story, with the various stages of development put into perspective. The preparation of Dynamic Fracture Mechanics turned out to be among the most satisfying experiences of my professional life. A good deal of the credit for the fact that such a specialized book is still in print after all these years goes to condensed matter physicists who discovered the subject for themselves during the 1990s.

The second noteworthy turn of events was another step in the increasingly productive interaction between solid mechanics and materials science. Two colleagues at Brown had founded a company concerned with fabrication of photovoltaic solar cells. These are thin film semiconductor diode structures that combine the effect of excitation of electrons from their ground states by photon absorption with the conduction band offset properties of PN junctions to produce electric current from sunlight. Their films were peeling off the substrates and they wanted to know the reason, which was easy enough to explain.

More importantly, from the literature of the day it was clear that issues of stress driven degradation of material quality loomed as barriers to the advancement of a number of promising thin film technologies, even in cases in which load carrying capacity of the film material wasn't a design function; mechanics issues were literally showstoppers. Many interesting questions were identified that could be addressed by applying the principles of mechanics, possibly extended by coupling with thermodynamics, microstructural features or quantum mechanics. The appeal of this new area suggested it was time for another change in focus. As Yogi Berra advised, "When you come to a fork in the road, take it." Through this thin films research effort, I came to know a whole new group of very capable people working with semiconductor materials, including crystal growers, microscopists, and device engineers. After working in the area for a dozen years or so, and after teaching a graduate course on thin films several times at Brown, it seemed that there was a story to be told and another book was in order. Subra Suresh joined me in the project of writing Thin Film Materials which, we're happy to report, is now completed. This book writing experience has again been exceptionally rewarding, in large part due to Subra’s good company.

So much for the past. What about the future for mechanics? In the course of my career, the field has been sustained largely by two major movements -- the evolution of the numerical finite element approach as a core methodology and the central role of mechanics in quantifying material performance, the latter of which contributed to a welcome rejuvenation of experimental mechanics. It's interesting to speculate about emerging trends, although one wonders about the wisdom of doing so in front of a microphone. It's likely that mechanics applied to small-scale engineering materials and biomaterials will continue as a guiding beacon for some time. By relying on its very special perspectives -- continuous field concepts, microstructurally informed constitutive modeling, quantitative analysis and experimentation, and emphasis on realistic boundary constraints -- mechanics can continue to serve as a critical link between the basic sciences and engineering applications. To pursue opportunities, it's incumbent upon us to develop a certain depth of understanding about mechanics related questions in other fields. I would agree that there is nothing as useful as a sound fundamental mechanics theory, but that utility can be appreciated only through demonstration. Someone has to care about the consequences.

It is important that we, as custodians of the discipline, sustain its core structure. To me, this means having a significant number of strong, vibrant graduate programs around the country that offer comprehensive educations spanning theory, computation and experiment. The detailed structure of such programs today differs markedly from those in my own student days, and it seems that we are in the early stages of another significant transition. In a decade, I expect that other issues, for example, thermodynamics, statistical mechanics and surface phenomena, will become more central than they are today.

Both John Hutchinson last year and Ted Belytschko the year before emphasized the importance of cultivation of young people for the vitality of the field. Observing young people I've known thrive in their endeavors, and thereby become not-so-young leaders in the field, is always satisfying, and I certainly agree with the viewpoint. There are other aspects of our field on which I've formed views over the years -- the role of the archival literature, for example -- but I don't wish to overstay my welcome at the podium. Therefore, I'll conclude with a couple of acknowledgments.

A professional career is rarely a solitary endeavor, and that is surely so in my case. There are many people who have earned a portion of the recognition handed to me tonight. Most important among them are the members of my family who have given a deeper purpose to it all. In her own way, my wife Colleen has been a contributor to the field of mechanics since our days in Evanston; in addition, her character and good sense have often offset my own shortcomings.

I feel very fortunate to have been a member of this mechanics community over the years. The largely open, constructive and scholarly character of the community has been a sustaining strength, even though its cast of characters changes continuously. It's been my great privilege to have worked closely with many superb colleagues and students at Brown University for many years. When all is said and done, the real satisfaction of standing here tonight has been in the journey itself.

It's a great honor to be included in this ongoing tribute to Stephen Timoshenko. I'm very grateful to the Applied Mechanics Division executive committee and to all who have contributed anonymously to bringing this about. Clearly, these are all honorable people, in spite of the fact that they've exaggerated the truth so as to make this seem plausible.

In a recent PBS broadcast on Winston Churchill, it was reported that, when he set out to prepare his six-volume history of the second world war, he said, "History will be kind to me, for I shall write it." I am very grateful to have had the opportunity to write a bit of my own history here this evening. Thank you all for coming.

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