Pergamon Int. J. Impact Engng Vol. 18, Nos 7 8, pp. xv xx, 1996

Copyright '~: 1996 Published by Elsevier Science Ltd Printed in Great Britain

TRIBUTES

Greetings on your 80th birthday. Hard to believe so much time has passed since we started to work together forty years ago. Indeed it was in September 1956 that I arrived at Brown University as an Assistant Professor and you were part of the "establishment" there. At the suggestion of Dan Drucker, then Chairman of the Engineering Division, I jumped into experimental work and found it fascinating.

Looking back, I think the experimental work we did together was fairly important to the development of the field of Dynamic Plasticity of Structures. The situation in the field in the late 50s, the 60s and even in the 70s was much less clear than it is today, and well planned and carefully performed experimentation did much to clarify the situation. I think we both derived considerable satisfaction from those efforts.

On this occasion, I wish to offer my congratulations to you on the totality of your important work on Dynamic Plasticity of Structures. Your work not only motivated other investigators but was directly useful to practicing engineers which is really the end objective of academics in the field of engineering.

With all best wishes for your continued ability to be scientifically active.

SOL R. BODNER Markus Reiner Professor of

Mechanics and Rheology Faculty of Mechanical Engineering

Technion-Israel Institute of Technology Haifa, Israel.

We spent almost one year working with Professor Paul Symonds at the Division of Engineering at Brown University in 1987-1988. It was a particularly stimulating period of time in our lives. We were at the end of our doctoral studies and, for the first time, were experiencing an advanced academic environment, different from our original schools, as autonomous and responsible subjects. The acquaintance with Professor Symonds, his experience in research, his profound and at the same time simple and direct understanding of complex mechanical phenomena and, most of all, his extremely rich personality deeply influenced our way to approach research and to understand the academic profession.

Besides his outstanding capacities as a researcher, we had the opportunity to appreciate his broad culture on various fields of human activity which he let emerge during the conversa- tion in a pleasant and gentle way, always tempered by a very special sense of humour.

For his intellectual honesty, for his attention to social issues and for his kind and friendly attitude, he represents for us an example of gentlemanly behaviour and a model to which we wish to tend (probably only asymptotically) in the future.

GUIDO BORINO UMBERTO PEREGO

Universita di Palermo, and Politecnico of Milan

Italy

About four years ago Professor Symonds, through Professor Maier, invited me to work with him for a period of six months at Brown University on the topic of chaotic dynamics of

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a fixed-ended beam, now known as "Symonds beam". It was at this time that I became aware of his interesting personality.

When I arrived at Brown I only knew a few words of English. In spite of this, I was able to communicate with the Professor, speaking a mixture of English, French and Italian. He was always very patient and tried to interpret what I was saying and communicated in a way that was easy for me to understand often repeating the same sentence in two or three languages. Besides his great patience, other aspects of his personality impressed me, including his generosity and his hospitality that proved to be very noble, kind and refined; these are qualities that are more and more difficult to find today.

Many people often speak of his sense of humour. Unfortunately, because of my difficulty in English, I wasn't able to understand all of it but through his particular way of smiling and from his facial expressions I always understood that he was a very humourous person.

In addition to his great human qualities I would also like to thank Professor Symonds for the scientific enrichment that I received from him and also for the particular way of doing research that has helped me very much even after my return to Italy.

ANGELO CARINI Department of Civil Engineering

University of Brescia, via Branze, 38 25123 Brescia, Italy

Visit to the USSR in 1990

In the last 12 years Prof. Symonds has intensively studied special features of the dynamic behavior of complex nonlinear systems. He was also interested in Russia because it is not a simple country. Therefore when the dynamics of the development of the USSR acquired in 1989-90 counterintuitive and unpredictable character he decided to observe some peculiari- ties of the chaotic development of this complex system with his own eyes and arrived in the USSR with a scientific visit.

He was "lucky" in Kiev because he met me. I did not know any English and successfully used this fact to introduce additional elements of chaos and unpredictability in the life of Prof. Symonds. However the Symonds have not lost their heads in this intricate situation. They counteracted me and the chaos of the surrounding life with self-possession, hopes for a happy return to the USA and the medical skill of Mrs Symonds.

I will illustrate the aforesaid by a recollection of one evening. We were going to a concert. As soon as we left the hotel Prof. Symonds hurt his foot, but we went on our trip. However when we left the taxi we saw that we were not taken to the church where the concert was to take place. What is more I did not know the address of the right church! AU evening we walked and drove but did not find the church. We went to the hotel very late and I realized that Prof. Symonds foot was swollen and he could hardly walk. I felt very bad but not because of tiredness!

The accident with his foot did not have any consequences thanks to the medical skills of Mrs Symonds. I think Prof. Symonds remembers also some other days in Kiev and in Leningrad where we were for a week because anomalous and unpredictable situations stick well in our memory. Possibly these situations allowed Prof. Symonds to form a new view of some of his scientific research!?

I remember these days, I was very privileged to take care of an intellectual who understands well imperfections of the world and its people. Is it possible that this understand- ing makes Prof. Symonds' humor a little dry?

Shamil U. Galiyev (now at) Department of Mechanical Engineering

The University of Auckland Private Bag 92019

Auckland, New Zealand

T r i b u t e s x v i i

Professor Paul S. Symonds welcomed me to collaborate with him when I was very young. I had very little experience in research work, and almost none in the field he was at that time exploring. I was visiting the U.S. for the first time, and I had to learn English,just to start with. At the time I was (and still have a tendency to be) very rash and impetuous. Also, he did not know me at all.

Despite all these difficulties, Professor Symonds received me with great warmth just out of his wonderful spirit. In the year I stayed at Brown University he taught me, in his shy and fascinating way, how to be patient, how to approach problems, how to write a paper. The best part of it, however, has been his spirit. His constant--and somewhat British, may I add-- tendency towards the understatement stands out, in my mind. Also, I was impressed by his wide horizon of interests, which include enjoying music and reading, a strong social commitment and a passion for learning new things, no matter when and why. Examples? I still remember the sheer fun I had when he brought me in Boston to see "The Mikado" by Gilbert and Sullivan, where his son was in charge of the whole lighting business, and where everybody involved seemed to have even more fun that the spectators. I also remember him calling Henry Fielding's Tom Jones "an old English chestnut". As for the social commitment, it may be interesting to recall that he wrote at least one strong article, in the Providence Journal, against the Star Wars Programme which, at that time, President Reagan was trying to sell to the world. Professor Symonds also took every Friday morning to bring meals home to old and ill people, helped in this by his wife Ilese.

Professor Symonds has been for me a wonderful, albeit unreachable, example of both a scientist and human being; I hope that many more young men and women will enjoy, as I did, both the long silences in his office and his smile. I think that now, when he is turning 80 it is a good time to say again "thank you".

FRANCESCO GENNA Professor of Civil Engineering

Department of Civil Engineering University of Brescia, Italy

Paul's Magic Number

Plasticity and more exactly visco-plasticity is a highly nonlinear topic. This is why so many people were, and still are, interested in this branch of Theoretical and Applied Mechanics. After thousands of publications in this field, and many decades, Paul's early contributions have stood the test of time. One of those contributions which I would like to mention is the citation [1 ] of this note, where a simple constitutive equation, called the "Cowper-Symonds Formula" has been introduced; this was in 1957!

/~ O" o r O" = -'t- - - o[l \~o7 d"

The Magic Number is associated with q. It happens that for many metallic materials it is a constant describing well the rate sensitivity n = l/q. My personal curiosity about this equation, and the Magic Number q, was completely satisfied when I analysed my results of torsion tests performed over a wide range of strain rates on technically pure iron [2]. Indeed, the rate sensitivity n and the Magic Number varied only slightly with shear strain, that is 0.2 > n > 0.169 and, respectively, 5.0 < q < 5.92 for the range of strains 0.015 < F < 0.4. The Magic Number of mild steels is estimated in the literature as q = 5, for example [3]. Other materials also obey the constancy of the Magic Number!

After almost 40 years the equation discussed here and the Magic Number q can be found in many modern Finite Element codes, including ABAQUS.

xviii Tributes

I wish to Paul, and Ilese, on the occasion of his 80th birthday many years ahead of happiness, good sense of humor and well being. The Magic Number will stay forever!

JANUSZ R. KLEPACZKO

Metz University France

[1] G. R. Cowper and P. S. Symonds, Strain hardening and strain-rate effects in the impact loading of cantilever beams, Brown Univ. Div. of Appl. Math. Rep. No. 28, September (1957).

I-2] J. R. Klepaczko, The strain rate behaviour of iron in pure shear, Int. J. Solids and Struct., 5, 533 (1969). [3] N. Jones, Structural Impact, Cambridge Univ. Press (1989).

In his quiet way, Paul has had a big impact on the people who have known and worked with him. Besides knowing and cooperating with him ever since I arrived at Brown University from England in 1948, my wife Shirley and I have had a long association with him and Ilese. During the 1950s, we had numerous family outings together when their and our children were young, and we have followed with interest their subsequent activities. We all of course have a special interest in England, where their younger son found his life as an archaeologist.

Although I have not worked with Paul since leaving Brown in 1962, I do remember our joint effort in editing the book Plasticity, Proceedings of the Second Symposium on Naval Structual Mechanics, published by Pergamon Press, 1960. t

As a fellow octogenarian, I salute Paul for his work. Those early years at Brown certainly laid the basis for interesting years of work and research for both of us.

ERASTUS H. LEE

Professor Emeritus Stanford University

California U.S.A

It gives me great pleasure to write a tribute to Professor Symonds on his 80th birthday. For more than 40 years he has been an outstanding specialist in the field of dynamics of non- elastic structures. The year 1966 was very important in his scientific career when in a joint paper with J. B. Martin he worked out the method of modal solutions. This opened up new horizons for approximate solutions of the response of rigid plastic structures and is still a valuable technique nowadays. In his subsequent papers he developed this method to include elastic and viscous effects and geometrical non-linearities.

I have looked through many of Professor Symonds' papers and used them in my own research. We also corresponded and exchanged reprints of our papers. Personally we met first in 1989 when we both attended a conference in Poland. After this conference Paul and Ilese paid a short visit to Estonia. This was the time when the movement to free Estonia was at it's peak. They both had a friendly attitude to the fight for Estonia's freedom and up to now have been very interested in the life in Estonia.

Professor Symonds organised for me the excellent opportunity to work for two months in 1991 at Brown University under his leadership. At this time he had discovered the effect of "counter-intuitive behaviour" of beams under pulse loading and was trying to clarify whether or not the vibrations of the structure are chaotic. Although the problem of chaotic motions was at this time quite new to me, I found it very interesting and got great satisfaction from this work. During these two months I realised that Paul was not only an outstanding scientist, but also a man with an open heart. When somebody had difficulties he tried to find

Tributes xix

possibilities for helping him. Paul's simplicity, hospitality and friendly attitude remain unforgettable to me.

I.JLO LEPIK Professor Emeritus

Tartu University Estonia

As everybody knows, in the 1950s, plasticity was a booming area central to the whole of applied mechanics and Brown University was irradiation center of plasticity, in my recollec- tions its capital or its main temple.

You were there, in the leading team: Prager, Drucker, Symonds and a few others. Your favourite research subjects were plastic dynamics, structural responses to impulsive loading, shakedown under variable repeated loads.

The scientific subjects you pioneered at the beginning of the second half of this century and so effectively investigated and promoted in the subsequent decades, are still lively research topics at the approaching end of this century, but other exciting topics emerged in the last few years: among these chaotic and "counterintuitive" manifestations in nonlinear dynamics, to the understanding of which your recent work has contributed so much.

Your seminal papers, your outstanding scientific achievements, your leading role as educator and researcher for decades in a major university, are acknowledged with deep appreciation by the whole international community of structural mechanics.

However, I have enjoyed your and Ilese's hospitality and friendship; I had opportunities to know your calm, thoughtful, unpretentious manners, your sense of humor, your intellectual honesty, your tolerance and helpfulness for the weaknesses of others, your kindness and generosity: briefly, your fascinating personality.

Therefore, I join the hommage so deservedly paid to you by a vast group of colleagues, friends and former students, with a very personal feeling of admiration and gratitude.

Ad multos annos, Paul, ad multos annos!

GIULIO MAIER Politecnico di Milano

Italy

I was a student of Professor Paul Symonds at Brown University. My thesis was on impact on a cantilever beam with strain rate sensitivity. I stayed on the faculty at Brown for three more years after I received my Ph. D. After I left Brown, my research interests changed to viscoelasticity, plastic waves, nonlinear elastic waves and, in the past 10 years or so, anisotropic elasticity and composites. Because of these, most people were surprised when I told them that I was Ph. D. student of Paul. Even though most of my research has very little to do with my Ph.D. thesis, I was fortunate to have Paul as my advisor. What he taught me was not only on impact on a cantilever beam. He taught me how to identify the core of a problem. He taught me means to simplify an otherwise untractable problem. These are essential in research on any subject.

Among Paul's many important and significant contributions, the discovery of the negative final displacement of an impulse loaded beam is most amazing. The final displacement of the beam is opposite to the direction of the applied load! This puzzling results has attracted the attention of experts as well as non-experts like me. In several of his presentations, the room was jam-packed with a revered and curious audience.

Paul is a warm and kind person with a sense of humor. At an ASME meeting in Chicago in 1976 Paul was the chairman of a session. He started the session by announcing that "--. each

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speaker is allowed 20 minutes for presentation and five minutes for discussion. This is Chicago. Anyone who speaks overtime will be shot to death on the spot." The session ended on time. At the Fifth International Symposium on Dynamic Plasticity held in Osaka, Japan in July 1995, I disclosed to Paul that there will be a Symposium in honor of his 80th birthday in 1996. "Do you really want to do that? ......... What's the matter with you, Thomas?" I told him that the Organizing Committee of the Symposium consists of Norman Jones, John Martin, Tom Wierzbicki, and myself. "I see," he paused. "You are the only American."

T. C. T. TING Professor of Applied Mechanics University of Illinois at Chicago

Chicago, IL U.S.A.