Preface

Kumbakonam Ramamani Rajagopal

This collection of invited papers is being published in honor of our distinguished colleague, Professor KR Rajagopal. We wish to honor and celebrate his prodigious contributions to continuum mechanics over close to four decades. Raj, as he is affectionately known, has thus far authored (or co-authored) approximately 500 scientific papers and has mentored more than 40 doctoral students. At Texas A&M University, he currently holds appointments in five separate departments—Mechanical Engineering, Mathematics, Civil Engineering, Biomedical Engineering, and Chemical Engineering.

KR Rajagopal was born in New Delhi on 24 November 1950 into an orthodox Brahmin family. There were strict dietary restrictions: some family members would not even eat vegetables that grew below the ground. Also, there was a serious restriction on overseas travel.

Both of Raj’s grandfathers enjoyed distinguished careers. His mother’s father, VS Sundaram, was a Government Civil Servant before India gained Independence. Extremely gifted intellectually, but having no training in law, he authored the first book on Indian taxation laws, entitled “The Law of Income Tax in India,” which ran through several editions. He was honored by the British with a CBE. Raj fondly remembers having many heated arguments on philosophy with this grandfather. Raj’s father’s father, KS Rajagopala Iyengar, was a leading Civil Advocate.

Raj’s own father, KR Ramamani, studied physics at the university, but after the death of his father, he decided on a career in taxation law. He became widely known in India for his expertise, worked on later editions of VS Sundaram’s book, and taught courses on taxation at the Madras Law School. A firm believer in the liberating power of education, in 1996 KR Ramamani founded a free English-medium school in an economically downtrodden rural area north of Madras. ¹ Raj grew up fully expecting to follow in his father’s footsteps, but fortunately for continuum mechanics, fate decided otherwise. From his father, he also inherited a great appreciation for poetry.

Raj’s mother, Hemalata Sundaram, married young but pursued studies under Sanskrit scholars and philosophers. She published two books on the interpretation of Indian sacred texts. She also won awards for developing innovative farming techniques, including the cultivation of new strains of rice.

As a child, Raj developed the habit of challenging authority, a trait that many of us admire him for. He was not particularly interested in school, relying on his natural abilities to succeed. However, he was fortunate to attend an innovative primary school in Mylapore that had just been started by the Mylapore Women’s Club. His teacher in mathematics was a sister of the famous astrophysicist S Chandrasekhar. Another notable connection is to the phenomenally gifted mathematician, S Ramanujam, who once lived in the same town, Kumbakonam, from which Rajagopal takes his first name. South India has given the world more than its fair share of extraordinarily gifted individuals.

As a student, Raj was not an advocate of studying for examinations. Nevertheless, he achieved a distinction in mathematics, physics, and chemistry in the Pre-University Examination. He advanced to the Indian Institute of Technology, Madras, in 1968 for a five-year program in Mechanical Engineering. Still not a believer in cramming for exams, he once showed up for an examination that he expected to be on physics, but was on the calculus of variations instead! He graduated in 1973 with First Class Honors.

On his grandfather’s advice, Raj agreed to travel to the United States to obtain a Master’s degree prior to pursuing the family profession in India. However, on his very first night in Chicago, he experienced an epiphany. Lying sleepless in a downtown YMCA, the 23-year old Rajagopal began to question the path that his life appeared to be following. It suddenly became clear to him that he must immediately develop his own individual ambitions rather than follow the path of his father and grandfather.

Following this dramatic realization, Raj’s attitude towards his studies became serious and focused. During the academic year 1973–1974, he pursued an MS degree in Aerospace and Mechanical Engineering at the Illinois Institute of Technology. There, he was inspired to study continuum mechanics by the courses on elasticity and related topics by Professors LN Tao, RR Huilgol, and Barry Bernstein. Also at this time, he became aware of the works of Clifford Truesdell, which have had a lasting effect on him. He was struck by Truesdell’s emphasis on clarity of expression (both mathematical and literary), rigor, elegance, and generality. From reading Truesdell, he developed the habit of studying the original sources rather than relying on secondary ones and he came to have a deep appreciation for the culture and history of Natural Philosophy and Rational Mechanics.

Rajagopal returned to Madras in the summer of 1974, soon to discover that his mother, in her maternal wisdom, figured that it was time for him to find a suitable wife. After a flurry of consultations and detailed comparisons of horoscopes, among the many eligible young women one particularly stood out: Chandrika Iyengar, who was not only a Jawaharlal Nehru Gold Medalist at Delhi University but also the top student at the Delhi School of Economics; in addition, she was talented in languages, debating, and acting. Previously, she had attended a British school in Bangkok, where her father had been stationed as Regional Director of the Civil Aviation Organization. With not a little trepidation, Raj traveled to Delhi to meet the young lady, and was immediately swept off his feet. Happily, the feeling was reciprocal, and the engagement was announced in due course.

In the fall of 1974, Rajagopal moved to Minneapolis to pursue doctoral studies at the University of Minnesota. His research supervisor was Professor Roger Fosdick, in the Department of Aerospace Engineering and Mechanics, who also was his teacher in courses on continuum mechanics and thermodynamics. He was also deeply affected by the gifted Hungarian mathematician, Professor Steven A Gaal.

The following summer, Raj traveled to India to be married. The preliminary and main ceremonies spanned several days, culminating on 14 July 1975. Chandrika joined Raj in Minneapolis, where she studied for her PhD in anthropology. Her dissertation was concerned with the significant differences that exist between how Hinduism is perceived on the one hand by Western scholars, using such concepts as “sect” and “caste,” and on the other hand by Indian gurus and disciples themselves, who see it more as a living, evolving tradition. Chandrika gave birth to the couple’s first son, Keshava, in 1976. Raj completed his PhD dissertation in 1978, in which he presented a thermodynamical theory for the stability of Rivlin–Ericksen fluids.

During the next two years, Rajagopal held post-doctoral positions at the University of Michigan, Ann Arbor. Here began an intense collaboration and deep friendship with Professor Alan Wineman, which continue to this day. ² In 1978, Chandrika gave birth to a second son, Sudarshan.

It was during this period that Raj met Michael Carroll. Besides their love for finite elasticity and difficult mechanics problems of all sorts, the two shared interests in literature and cryptic crossword puzzles. Through Carroll, Raj was introduced to Michael Hayes, and a long-lasting bond with the Irish mechanics community was forged. A frequent lecturer thereafter in Ireland, Raj was overjoyed when asked to present a one-hour lecture at the Stokes’ Death Centenary Meeting in Dublin in 2003. ³

In the fall of 1980, Rajagopal was appointed Assistant Professor in Mechanical Engineering at the Catholic University of America. In 1982, he moved to the University of Pittsburgh, where he remained until 1995. His main position was in the Department of Mechanical Engineering, but he also became a Professor in the Department of Mathematics and Statistics, and a Professor of Surgery in the School of Medical and Health Sciences. At the beginning of 1996, Rajagopal became Forsyth Chair and Professor of Mechanical Engineering at Texas A&M University. Shortly thereafter, he was awarded a joint appointment in Mathematics. In 2002, he added the title of Professor of Biomedical Engineering. The Civil Engineering Department was next to appoint him (in 2003), and after that, the Chemical Engineering Department (in 2008). In addition, he became a Senior Research engineer at the Texas Transportation Institute at Texas A&M University.

Rajagopal’s research interests encompass an extraordinarily wide range, which I can only briefly sketch. In the area of nonlinear elasticity, he and his co-authors have discovered several new exact solutions: see, for instance, the papers [4 –6]. In addition, novel types of elastic behavior have been identified and studied [7 –9]. In the memoir [10], Rajagopal delves into the complexity of the concept of elasticity, quoting generously from Boyle, Hooke, Young, Lord Kelvin, Love, Truesdell, and other original thinkers.

A fertile topic of abiding interest to Rajagopal is that of implicit constitutive equations, with multiple branch solutions in general and evolving reference configurations. These ideas have led to new developments in several areas of solid and fluid mechanics [11 –19].

The behavior of non-Newtonian fluids has occupied Rajagopal throughout the years [20 –25]. With Truesdell, he has co-authored a fine textbook [26], which covers Rivlin–Ericksen fluids in addition to the usual Navier–Stokes and Euler fluids.

Rajagopal has devoted a great deal of effort to mixture theory [27 –31]. He and Tao have co-authored a book [28] on the subject, which includes chapters on diffusion of a fluid through a solid undergoing large deformation, and mixtures of two Newtonian fluids. Raj dedicated this book to his parents.

In the area of biomechanics, Rajagopal has worked on problems in hemodynamics [32 –34], arterial mechanics [35], and biological growth [36,37]. Rajagopal and co-workers have also devoted considerable attention to electromechanical materials [38 –41], geomaterials [42 –45], and traffic flow [46 –48].

A recent paper of Rajagopal’s challenges the dogma that bodies must always have particles as elements, and suggests instead that a point-free topological framework be developed [49]. ⁴ He sees this as having relevance for certain problems in continuum mechanics.

Professor Rajagopal has received numerous honors. At Texas A&M, he is both a University Distinguished Professor and a Regents Professor. He is a Fellow of the American Society of Mechanical Engineers and also a Fellow of the Indian National Academy of Engineering. His alma mater in Madras has recognized him both as an Outstanding Alumnus and a Distinguished Professor. The University of Pretoria has bestowed both an Honorary Doctorate and an Extraordinary Professorship upon him. Likewise, the University of Witwatersrand has conferred an Honorary Professorship. From Charles University in Prague, he received a Memorial Medal, followed by an Honorary Doctorate and an Honorary Professorship. He was also awarded an Honorary Doctorate by the Gheorghe Asachi Technical University of Iaşi. He is a recipient of the Eringen Medal from the Society of Engineering Science (2004). For his outstanding contributions to mechanics education, he received the Archie Higdon Distinguished Educator Award from the American Society for Engineering Education in 2005. Several scientific journals have devoted special issues to acknowledge Rajagopal’s contributions to mechanics and applied mathematics. ⁵

Professor Rajagopal is Co-Editor-in-Chief of the International Journal of Engineering Science, and serves (or has served) on the editorial boards of over 50 journals. ⁶ He was Chairman of the Society for Natural Philosophy from 1989 to 1991.

All of us who have interacted with Raj appreciate his exuberant passion, boundless energy, and unbridled enthusiasm for mechanics (and indeed for all things intellectual). The authors of the present collection offer their contributions as an expression of the high esteem in which they hold him.

At home, Raj is admired and cherished by Chandrika, his sons and his six grandchildren. ⁷ All over the world, and especially in the United States and India, he has a myriad of well-wishers.