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Speech of Acceptance of the 2017 Timoshenko Medal by Viggo Tvergaard

 Viggo Tvergaard

Mechanics in Denmark

Applied Mechanics Division Banquet, Tuesday, 7 November 2017

It is a great honor for me to receive the Timoshenko Medal. In particular I am very impressed when I look at the names of those who got it before me. Many thanks to those who have nominated me, and to those who have selected me for this honor.

Already during my PhD studies I read Timoshenko’s autobiography “As I Remember”. Strong early career, obtaining chairs in Strength of Materials in Kiev and in St. Petersburg. Interrupted by the russian revolution, and then a slow build up of his second strong career in the US. Very  impressive.

The Technical University of Denmark, where I studied, and where I work, is an old respected technical university. In international rankings we are often among the 5 to 10 best technical universities in Europe. The university was started in 1829 by the physics professor Hans Christian Oersted.  He was the scientist who discovered electromagnetism. During my studies, many departments still had rather little research; it is much better now where the level is kept up by strong competition. But, for my final year I had found two groups that were very active and had focus on applying mathematics. One was solid mechanics, the other was operational analysis and statistics. I had thought of continuing with the latter, but then my solid mechanics professor, Frithiof Niordson, asked if I would do a PhD study with him. When that had finished he asked if I would like to start as an Assistant Professor, and it has continued about like that.

Frithiof Niordson had studied in Stockholm, at professor Folke Odqvist who was an internationally active scientist in our field. Frithiof went to Brown University right after the second world war to get a PhD with Bill Prager. Frithiof was very smart, and he also had the ability to develop strong networks, e.g. with Bernie Budiansky who was his co-student at Brown and became a lifelong friend. Through this network I met Bernie’s student, John Hutchinson, and John’s student, Alan Needleman, two persons who have had strong influence on my research work, and who have become close friends. Frithiof spoke fluently Russian.  His mother was Russian, and from his Russian network I later developed close contacts to Grisha Barenblatt.

For the PhD I worked on a generalized beam theory that could describe unusual phenomena seen experimentally in a Swedish turbine factory. It was interesting enough, and I published two papers in Solids and Structures, but nobody cared and nobody cited it, except that in my second paper I must have cited the first one. Still most of a year of my PhD stipend was left. I was very interested in elastic post-buckling theory, and I asked John Hutchinson, who was then a visiting professor, about a problem I could use to learn that. He mentioned a nice problem on non-linear mode interaction in post-buckling. But two days later he asked me to wait, because it was really an idea he got from Warner Koiter. Shortly after, I got a very kind letter from Koiter, in which he said that it would be interesting to see my results, and that he would probably also work on it himself later on. He did, a couple of years later. After that, for the next about 25 years, whenever I met Koiter, he was always very supportive and took interest in my work.

In May 1971, I went to my first Congress, CANCAM 3 in Calgary. This was my first time in an airplane. I heard Koiter lecture on elastic stability. Den Hartog in a subsequent lecture used buckling of an oil drilling tube to tease Koiter by asking how a structure with only tensile stresses can buckle. And I heard a very interesting lunch-lecture by G.I. Taylor. I also met several other strong scientists who later got to play a role in my life. After the congress Frithiof had arranged a trip for me to visit some of his friends, in order to broaden my mind, I think. In the University of Seattle Carl Pearson received me for a day and showed me some of their research. At the Courant Institute in New York Joe Keller took care of me, and at Harvard John Hutchinson was my host. Here I also met Bernie Budiansky, Lyell Sanders and others. And afterwards John and his family took me along to New Hampshire where a bunch of their friends had planned a day trip of canoeing down through rapids. We were about 10 canoes. Clearly there were colorful sides to solid mechanics.

Several foreign scientists, most from the US, spent their sabbatical at our Department in the early 1970’ies. At that time Frithiof Niordson had started the Danish Centre for Applied Mathematics and Mechanics, DCAMM, which helped increasing the focus on our activities. In the fall of 1973 the visitor was Alan Needleman, who then worked as an Assist. Prof. at the Math. Dept of MIT.  We  decided to collaborate on a paper, it turned out we interacted very well and that we enjoyed it, so it has been going on ever since. In the first years it was plastic buckling of various structural elements, but it also developed into various finite strain problems and fracture problems.

In 1976 my family had bought a sailboat, and I started sail racing together with some PhD students. But we did not win. Therefore, for some months I took more interest in another type of mechanics, i.e. fluid dynamics, and I also communicated more with my fluid mechanics colleagues. One of the things I learned about, and used in the races, is the importance of the length of the laminar separation bubble at the front of the genoa.  It was only racing on a local Danish level, but at least after that we started to win some of our races.

In 1978 my colleague Jes Christoffersen and John Hutchinson developed J2 corner theory, a detailed description of the elastic-plastic response at a vertex on the yield surface. I had just defended the big old-fashioned doctor degree in Denmark, so I needed something else to do. John suggested that he and I should use the J2 corner theory to model surface wave instabilities on an elastic-plastic solid, like ocean waves with zero wave speed. We could relate that to experiments that John had just seen in Stockholm. The same year I did some unit cell model analyses for a porous plastic solid to try to estimate the accuracy of the recently developed Gurson model.

A very important trip for me was the half year sabbatical I had at Brown University in 1979. I was obviously there to collaborate with Alan, and we worked on buckling localization and on applications of the J2 corner theory programme. But also meeting and discussing with the very strong solid mechanics group at Brown was a great experience for me, Jim Rice, Ben Freund and Bob Asaro were all very positive and friendly. At the same time I could still work on a paper with John, as Harvard was only a short drive away.

After the sabbatical a long period started, where I visited at Brown every year, and Alan visited in Denmark every year. We worked hard to produce new research. In addition, at each visit to Brown it was very inspiring for me at to discuss mechanics with the colleagues who were there at the time, including Ben Freund, Subra Suresh, Michael Ortiz, Kyung-Suk Kim and Fong Shih.

During this period a friend of mine moved to a chemical company, Haldor Topsoe Ltd, located a few kilometers from my university. They are very interested in research, spending much money on that, but not solid mechanics research.  Their focus is on surface physics and chemistry to improve their expertise in catalysis. However, solid mechanics is a limiting factor, as some of the containers in their factories operated at 950 dgr C and at 35 atmospheres of internal pressure, and the chemistry inside would be more efficient under higher pressure and higher temperature. They asked if I would consult on creep rupture. Could be fun, all I knew about it was continuum damage mechanics following the ideas of Kachanov and Rabotnov. But reading about it I soon learned that Jim Rice had done very interesting micromechanical work, analyzing diffusive growth of grain boundary cavities, and that also Alan and John had contributed to the area. I could use these results to develop constitutive models and for some years I served as a permanent consultant to the company, being member of their Scientific Advisory Committee. During this period I got very involved in studying the works of strong materials scientists such as Mike Ashby, Ali Argon, Brian Dyson, and others.

In the years with my little extra job in the chemical company I published several papers on creep rupture, all single author papers. This probably is not so typical in our field, but while I much enjoy working with colleagues, and have worked with many different co-authors over the years, I also like working alone, and this covers a good part of the papers I have published.

We all do research all the time. It is exciting and takes all our effort. But, on and off something happens that interrupts the daily routine of teaching and research. About 30 years ago the President of our University telephoned me one day in January and said he would like to persuade me to give the Feast Lecture at the annual party of the University in April. He explained it had to be exactly 20 minutes, technical, popular and somewhat entertaining. After a moment's consideration I said yes. At least I would try something different. But as the time approached I became more nervous. The room can seat 1500 persons, and it was full. At the first row was the Queen of Denmark and her husband the Prince, together with members of the government, the ministers of education, research, etc, and many other important people. I used a couple of the experiences of G.I. Taylor, taken from his lunch lecture in Calgary, including his description of how pilots 100 years ago tried to find out what was up and down when they flew through a big cloud. Otherwise I mainly showed slides inspired by my own research, it seemed to work.

Around 1990 Erik van der Giessen asked if he could spend a year with me as a postdoc. He came from the group of professors Besseling and Koiter in Delft, and he was funded by the Dutch academy of sciences. I knew he was a young star, so I was very pleased to receive him. Indeed it became a very productive collaboration. We first continued the work on the micromechanics of creep rupture, and also did other things. After the first year Erik came back for about a week every year for a number of years.

Another of these interruptions of the daily routine happened one day in 1995 when I received a telephone call asking if I would join the Board of Directors of a Danish company, called Aalborg Industries Ltd, also known as Aalborg Boilers. In the afternoon the CEO of the company and a representative of the owners came and talked to me, and so I started doing that beside my research. The other board members were directors from Danish companies, and an earlier leader of the blacksmith union who was very well known by danes. They were not interested in solid mechanics.  We flew to meetings there 6 or 7 times every year, in the western part of Denmark. The company had close to 20 subsidiaries spread over the world, and bought one or two new ones every year. At the end we were bought, so this part of my activity ended. At that time, the company had an annual turnover of about 2 billion Danish kroner, and an annual profit of about 100 million D. Kr.  My conclusion afterwards was that this kind of activity gives an insight that would be good for every professor of mechanical engineering.

At about the same time a Japanese scientist, Mitsutoshi Kuroda, asked if he could come and spend a year with me. He came from a rather unknown private university, but I quickly learned that he was very strong and I realized that he would soon become one of the strongest plasticity researchers of Japan. Indeed soon after the visit he moved to one of the known state universities, where he is now a professor. We worked on topics relating to plastic flow localization, crystal plasticity, and non-local plasticity. In the years after the first visit Mitsutoshi returned several times for shorter visits, and it has been very productive for both of us.

IUTAM, the International Union of Theoretical and Applied Mechanics, has played a rather big role throughout my professional life. Our department head for many years, Frithiof Niordson, was very active in the Bureau of IUTAM, and he argued that this organization is very important for representing our field internationally, for keeping our subject visible and for supporting international collaborations. I took the same attitude, and whenever asked to do something for IUTAM I have said yes, many different kinds of duties. Therefore, when I was asked in 2012 if I would be willing to serve as the President of the Union, I also said yes, and did it for four years.

I have described that international contacts and collaborations have had a strong influence on my research activities. But naturally, most of my time has been spent as a teacher and researcher in Denmark. Among my teaching duties has been several first or second year classes with up to 200 students, so many thousands of previous students know me, and in the little country I live in I frequently meet some of them. It has been inspiring to be the advisor of many Master Thesis students, and of more than 20 PhD’s. In particular I would like to mention the four of my previous PhD’s who are colleagues in the solid mechanics group of our Department for Mechanical Engineering, Christian Niordson, Brian Legarth, Kim Nielsen and Ann Bettina Richelsen.  They are working hard on materials mechanics research with their PhD students. We also have strong research groups on topology optimization and on dynamics. I will add that in our group we also consider John Hutchinson and Alan Needleman part of Danish mechanics.

Finally, thanks for listening to this story about mechanics in a small country, and thanks for your patience.

Speeches by other Timoshenko Medalists


Mike Ciavarella's picture

Congratulations.  You seem to have lived a wonderful time for mechanics, and in very good company.


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