1994 Timoshenko Medal Lecture by James R. Rice

Notes of AMR Administrators. Posted today is the text of the lecture by James R. Rice, the 1994 Timoshenko Medalist, presented on 10 November 1994, in Hyatt Regency Chicago. You can also download a biography of Rice prepared by Tze-Jer Chuang and John W. Rudnicki


Timoshenko Medal Lecture
James R. Rice

It is a great pleasure to be here among so many old friends and colleagues, and to thank you for the recognition symbolized by this award. Especially, it is a pleasure to thank my dear friend Alan Needleman for his kind words of introduction.

Any mechanician must consider it a great honor to receive an award named for Timoshenko. Like for many others here, the sight of his classic black-covered books on elasticity and structural mechanics brings back pleasant memories of my earliest involvement in our field. A while ago my interest in the historical origin of ideas in mechanics developed more purposefully, in response being asked to prepare an article on Solid Mechanics for the Encyclopaedia Britannica. That led ultimately to close study of another Timoshenko book, one that I had known before just by browsing acquaintance, namely, his History of Strength of Materials, with a Brief Account of the History of Theory of Elasticity and Theory of Structures. That was published in 1953, when he was 75 years old. The preface revealed that for 25 years before that time, he had been lecturing to students on the history of concepts and ideas in solid mechanics, and on the careers of those from Galileo to his own mentor, Ludwig Prandtl at Göttingen, who shaped the subject into what was then its modern form. One cannot help but understand that Timoshenko cared in a deep cultural sense about his subject and those who shaped it, and that too adds to the pleasure of receiving this award named for him.

Now, what shall I say to you? I didn't suppose it was appropriate to seek guidance from my Harvard colleagues on that, but some advice came unsolicited from John Hutchinson, as chairperson of the Applied Mechanics Division. A few weeks ago he knocked on my office door, walked in, and announced "Remember, your talk is going to be in the Newsletter and we don't have much room, so keep it short". A little research revealed that he gave the same advice, "keep it short", to our friend Bernie Budiansky, when Bernie spoke on this occasion a few years ago, so perhaps John just feels that he already hears quite enough from the two of us.

This is an occasion on which some reminiscences, at least within John's guideline, could be allowed. I'd like to tell you a little bit about what I've experienced, and to draw some conclusions when I can.

It is difficult to reminisce over my own formative years without sensing the sharp contrast with the far more difficult situation faced by the young generation today. My generation, and especially my own narrow age range within that generation, had things easier, I think, than any group before or after. I entered Lehigh for undergraduate studies one year after Sputnik. It was a time when support for science and engineering was enlarging fast, when opportunities were abundant. There were plenty of graduate fellowships. There were also generous loan programs, fully forgivable for those who went into teaching. I had both at Lehigh, where I also stayed for graduate studies. Getting a postdoc position could be accomplished mainly by a few telephone calls. My first faculty appointment came when, in the midst of a first postdoc year at Brown, our chairperson knocked on the office door and asked if I would like to stay the next year as an Assistant Professor. I said yes and that was that. Promotion and tenure processes were not much more complicated.

But that was then, not now. To quote David Goodstein of Caltech, "We are at the beginnings of the end of the exponential expansion era of science [but we are] still trying to maintain a social structure of science (research, education, funding, institutions, and so on) that is based on the unexamined assumption that the future will be just like the past." I need hardly add that the signs of that exponential expansion of people, not matched by the same growth of resources and opportunities, are everywhere. That makes it incredibly more difficult today for young people, and also for many members of older generations who have had to face job loss or sharply reduced prospects.

I would like to give you some predictions of what more specific difficulties the future will bring, and of how our community should contend with them, but that inclination has to be tempered by another quote, one that I've heard attributed to Neils Bohr: "Prediction is very difficult, especially of the future." So instead I'll return to some reminiscences, although maybe the difficulty of prediction of things other than the future, to which Bohr alluded, makes that an uncertain venture too.

Undergraduate years: Ferdinand Beer at Lehigh had assembled an advanced and challenging program in mechanics for theoretically inclined undergraduates. He had the good sense to know that some independent minded students could be recruited by relaxing the incredibly rigid course requirements common in engineering programs of that day. John Hutchinson had been such a recruit to Ferd's program a couple years before me. Ferd had the help of some talented people, including a cluster of bright young faculty members then beginning their careers: Fazil Erdogan, George Sih, Gerry Smith, and Paul Paris. All of them made their mark in mechanics, and I was fortunate to have them all as teachers. They were good at it and great role models. I was to have a lot of fruitful interaction with Paul Paris, as did John Hutchinson too, in subsequent years in work on nonlinear crack mechanics.

Staying at Lehigh for graduate school was against the advice of my teachers, who knew that the place was hardly on the map in our field at that time (it became a lot more prominent after I left!). But Paris had returned from summers at Boeing with faith that there was something to be done on fracture and fatigue, using the stress analysis of cracks that George Irwin at the Naval Research Laboratory had been pushing, and he had already recruited Sih and Erdogan to the effort. What none of us understood is that we were, essentially, getting on at the ground floor, as this previously neglected area of fracture mechanics began its rapid and, we hope, effective rise towards its modern form.

This has always puzzled me: How do you recognize what topics will grow and blossom, and how do you figure out when, instead, you are committing yourself (and your precious students) to topics on which, at best, only small incremental additions can be made? That latter category inevitably includes most of the presently established, recognized areas within a field. The choice is not so easy at the time as it seems in retrospect. The established, or sanctioned, areas of study always attract lots of bright people, excited by the once-new discoveries that launched the area, and when the star of an area has risen, you do not find it difficult to explain to others why you are joining that area too. I was certainly not sure myself that this new area of fracture mechanics was a star that was going to rise. So while I worked with enthusiasm, even starting as an undergraduate student, on models for interfacial cracks and for plastic effects in fatigue crack growth, that was a hobby. I played it safe as regards what was going to be my Ph. D. thesis topic, and did that in the respectable field of stochastic processes. Well, no one references the work based on my thesis.

Ferdinand Beer pushed me out of Lehigh while I was still quite wet behind the ears. He felt that I had sampled what they had to offer, and called me into his office one day to hint that there would be no impediments to quickly wrapping up my thesis if I could get a postdoc at a place he recommended. His list was short: Brown or Harvard. I said that I had heard great things about Brown from some of my instructors, so I would like to go there, and he worked to see that a postdoctoral fellowship was soon arranged. That was a lot easier then than now, but we should all take Ferd's interest in his students as a model for how we should be looking after our own.

Brown was a great experience. True, when I arrived there in fall of 1964, some distinguished figures were packing their bags to go elsewhere and some were already gone. One was Bill Prager although, happily, he came back to finish his active career there before retiring to Switzerland; another was Eli Sternberg, and I had the pleasure of spending a little time with him on a sabbatical at Caltech in 1988 before his tragic death. But the talent still at Brown was deep. Dan Drucker was my postdoctoral host and mentor, and there was a marvelous group of mechanicians still in residence. Sadly, the last few years have not been kind to that group; of them, death has now claimed my friends Jacques Duffy, Joe Kestin, Harry Kolsky and Jack Pipkin. Also, on arrival in 1964, I found Brown awash with interesting visitors. Rod Clifton was just arriving to the faculty and over the years I was also to enjoy friendships and sometimes collaborations with such newcomers as Pedro Marcal, Ron Armstrong, Ben Freund, Jerry Weiner, Alan Needleman, Constantine Dafermos and Bob Asaro. So Brown managed to renew itself and stay in a leading position despite that exodus, and they certainly survived in good style my own exodus to a neighboring city in 1981, one that Constantine suggested, with a wink, might improve both institutions involved!

I learned much from Dan Drucker. We worked together on how to calculate energy changes of solids due to cracking or removal of material, a problem on which I had some results for the linear elastic case in some notes done at Lehigh. Dan opened my eyes on the importance of generalizing, of figuring out the widest class of materials and circumstances for which some theorem or procedure might be true. That lesson was put to good use in a short time, when the path-independent integral of crack theory was to emerge as I tried to generalize a formula for the energy release rate in crack growth that I had derived for a particular nonlinear elastic material, one whose stress-strain relation mocked ideally plastic response. That integral was discovered independently around the same time by Genady Cherepanov of Moscow, and both of us were soon to learn that, while it had apparently not occurred to him to apply it to cracks, the integral had been developed much earlier by Jock Eshelby of England as a way of calculating forces on heterogeneities and dislocations. We all could have profited, as Jim Knowles and Sternberg later pointed out, by having learned about what Emmy Nöether did in 1919, on associating conservation integrals, like the J integral, with variational principles. Budiansky and I were able to link the new conservation integrals emerging in that way to energy release rates.

Fracture mechanics turned out to be a major catalyst in bringing about the modern union of mechanics with materials science and engineering. The signs of the health of that marriage are evident in several of the AMD sessions I've been to at this conference. I think it must be difficult for modern students to understand the remarkable isolation that existed, at least in the USA, between people in materials, which was mostly called metallurgy then, and people in mechanics. The mainstream opinion in both camps seemed to be that they had nothing to learn from one another. Drucker wanted to change that. I was fortunate to have many contacts also in my early years with Frank McClintock, who was nearby at MIT, and he thought that isolation a scandal. I was happy to sign on as foot soldier to their cause, but the task turned out to be an easy one because, despite mainstream opinion, many willing hands were to be extended from the materials community. My work on elastic-plastic fracture in relation to microscale ductile void growth processes was in furtherance of a program for which McClintock had laid the general outlines, and I had many other fruitful collaborations and contacts with people in materials science and metallurgy. Especially that includes Robb Thomson, and more recently Ali Argon, on atomic and dislocation-scale processes at crack tips, John Knott on microscopic mechanisms of cleavage fracture in steels, Bob Asaro on plastic flow localization, and some others that I'll mention shortly. A lesson I would draw here: We must ask where are there unnatural, unproductive separations between mechanics and other sciences or technologies, and what can be done to close them. Perhaps some current examples can be found.

Joseph Kestin at Brown engaged me, as a willing pupil, on thermodynamics, to which he insisted that all phenomena must march, and that we only had to figure out how to express that fact. That led me to concentrate more fully on some studies I had already begun, on how to relate inelastic deformation in solids to dislocation motion on the microscale. It was soon clear that it was simplest to think of dislocations, and other types of structural rearrangements, as corresponding to a thermodynamicist's internal variables, and that proved a useful route to formulating plastic flow at large strain and identifying general features of viscoplastic constitutive laws. I later worked with Rodney Hill on that area, during a sabbatical at Cambridge in 1971-72. Thermodynamic thinking proved extremely useful as I ventured more into materials science, and helped me address such topics as the embrittlement of material interfaces by solutes and mobile segregants like hydrogen, and diffusive processes of matter transport that are important for high temperature failure of materials. On those topics, I also had collaboration, or at least intense discussion, with some gifted materials scientists, including John Hirth, Mike Ashby, Greg Olson and Tony Evans. Further, the thermodynamic style of approaching problems, especially of making use of what we call reciprocity concepts in elasticity, stood me well in many other studies; they include figuring out the effects of shear faulting on the Earth's inertia tensor and gravity field, formulating what is called weight function theory in elastic crack mechanics, working out dislocation interactions with cracks and with one another, and figuring out ways of calculating J-integrals and energy release rates.

Pedro Marcal opened my eyes to computational mechanics, especially the finite element variety, and we directed students on applications to crack analysis and worried about how to deal with large plastic deformations. Alan Needleman was developing the same expertise as an outgrowth of his thesis work with John Hutchinson at Harvard, and we happily collaborated upon Alan's arrival at Brown, especially on a new class of problems of combined diffusion and plastic creep. Mostly, though, I just sit back and marvel at the computational challenges that Alan and some of his colleagues have mastered in describing flow and fracture phenomena.

Unbelievable as it may seem today, computational mechanics was an area viewed with suspicion, and even some disparagement, by many members of our community. Perhaps our reaction to the new has often been too hesitant. To be sure, we need to be discriminating, and nothing disturbs so much as those who jump on every passing bandwagon. But I think that we can draw a lesson on the importance of recognizing that the things worth doing in mechanics are not embedded in a rigid legacy. A healthy field is organic and fluid, always anxious to examine the new, to nurture it as needed, and absorb what has value.

Now, some words about those who have really done much of the work I've been talking about: I've been blessed when it comes to the gifted young coworkers that I've had as graduate students and postdocs. There was a marvelous group from my years at Brown. They have already made their individual marks, whether on computational methodology, fracture mechanics, materials engineering, rock mechanics, or earthquake processes, and are a great source of pride for me. There is a growing group from the Harvard years who will, I hope, be able to live up to that good example and, indeed, some have done so already. I am extremely happy to see many of them here tonight, and hope it will be alright to ask them to stand so that we can acknowledge them.

For most of the last 20 years I have been dividing my time between such materials themes as I've mentioned and problems on the mechanics of earthquakes. That earthquake interest began rather indirectly, through a collaboration with Andrew Palmer of Cambridge to study landslides in heavily consolidated clay soils, a problem for which it looked like concepts from fracture mechanics could play a role because the slip-rupture surface in such slope failures seems to slowly propagate up-slope like a thin shear crack. We soon were wondering what controlled the speed of propagation and, since soils in such conditions are inevitably water saturated, at least in England where we worked (that too was on sabbatical at Cambridge), interactions between the deforming material and the pressurization and transport of pore fluid was something that naturally came to our attention. Well, at about that same time, geophysicists working on earthquakes had become convinced that interactions between fluids and fault rocks, dilating as they failed, might be important in generating possible precursors to earthquakes. The commonality of the mechanisms under consideration was sufficiently tempting that I was soon heavily into those issues for earthquakes too, and that also was the start of a series of works I did on the mechanics of coupled deformation and diffusion processes in porous solids. Further, that interest in slip surfaces and faults, especially asking from where do they come, was the start of my studies on the localization of deformation into shear zones.

It turned out in light of better data and analysis over the next few years that the idea of dilatancy as a source of earthquake precursors faded. But there is still widespread interest in the interaction of fluids in fault zones, especially in connection with understanding the apparently low strength of some major faults, and that is a major theme in my present work. Here is another thing in which my students and coworkers in that area are now involved: We know that earthquakes are complex events in nearly every sense, including their irregular slip distributions in single events, magnitude distributions, spatial location patterns, and recurrences in time. We want to explain what we can of the origin of this complexity, and to use the statistics of seismicity and recent earthquake history, and crustal deformation measurements where available, together with physical modeling to assign risks of future events. There is now an active controversy over how much of seismic complexity is explainable from nonlinear dynamics acting on a smooth fault, and how much requires the observation that the array of faults on which earthquakes occur forms a complex fractal-like network.

Such issues for seismicity, and also complexity, self-organization and patterning in all manner of mechanical deformation and fracture processes, are topics which have also attracted many people from condensed matter physics in recent years. A definite movement that we see is that solid mechanics is becoming part of the agenda for many people whose field affiliation is physics; we can see signs of that too in some of the sessions at this conference. Such has long been the case for the fluid mechanics side of our house; the APS is a principal sponsor of activity there. Some of that is now happening in solid mechanics under the banner of materials physics in APS, accompanied with wide-ranging, one could even say uninhibited, symposium themes like "Slips, cracks and tears", and "Avalanches, fracture and related instabilities". We thus have an opportunity to make contact with a large theoretical and experimental community. To be sure, their level of education in continuum and fracture mechanics concepts is generally quite limited, so there will be much to learn from us, but so also do they have much to offer, in ways of understanding complexity, in novel theoretical approaches and experimental techniques, and in having a broad and fundamental agenda. So this should be good for all involved.

Well, I've tried to tell you something of my experience and sometimes to draw a lesson. Thank you for your patience in listening, although I must certainly have over-passed the length John wanted. Thank you once again for this honor, it being so much the nicer to receive it in this setting among so many friends and colleagues.