Memorial Tributes: Volume 19 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 19 BERNARD BUDIANSKY 1925–1999 Elected in 1976 “Contributions to the understanding of buckling phenomena, materials behavior, and new mathematical analyses of structural response.” BY JOHN HUTCHINSON BERNARD BUDIANSKY, an engineering scientist whose re- search and teaching shaped the fields of structures and the me- chanics of materials, died at the age of 73 on January 23, 1999, in Lexington, Massachusetts. No one who interacted with Bernie would fail to remember the delightfully opinionated, thought- fully probing, 6′4″ man with a large personality to match. Bernie’s career coincided with the US space effort and the expansion of engineering research in American universi- ties. His first technical job after college was at the National Advisory Committee for Aeronautics (NACA). From 1955 until his retirement in 1995, he was on the faculty in the Division of Engineering and Applied Sciences at Harvard University, as the Gordon McKay Professor of Structural Mechanics from 1961 and then as the Abbott and James Lawrence Professor of Engineering from 1983. His early research and consulting were heavily influ- enced by his exposure to developments in space structures at NACA (predecessor of the National Aeronautics and Space Administration, NASA). Many of his early contributions focused on plate and shell structures in studies of buckling, vibrations, and flutter. His research interests were as dynamic as his persona. Over his career, he made fundamental contri- butions to plasticity theory, composite materials, and many 39 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 19 40 MEMORIAL TRIBUTES aspects of micromechanics, including geophysical materials and biomechanics. As an engineering scientist, Bernie employed basic mechan- ics, the methods of applied mathematics, and numerical analy- sis to conduct his research. His career also spanned the growth of computer use in engineering, and he was at the forefront of this revolution. Bernie was born in New York City on March 8, 1925, to Russian immigrant parents. His father left the family when Bernie was a small child and he was raised by his mother and grandfather. He studied civil engineering at the City College of New York and graduated in 1944 at the age of 19. He retained a lifelong pride in the fact that his undergraduate college pro- duced so many of the nation’s leading engineers and scientists. At City College he honed his skills in mathematics and physics in addition to engineering. And his first job, in the Structures Research Division of NACA at Langley Field in 1944, turned out to be an ideal match for these skills and inter- ests. His first paper, on the elastic buckling of plates, launched him on the road to becoming America’s leading expert in the buckling of structures. During his NACA years (1947–1950) Bernie matriculated at Brown University, where he received both an ScM and a PhD, advised by William Prager. In his PhD thesis he invented the slip theory of plasticity, which led to new understanding of metal plasticity and, in particular, its application to struc- tures that buckle after they are loaded into the plastic range. His thesis spawned much follow-on research, especially in the Soviet Union. Some of the underlying ideas in the thesis had emerged from interactions at NACA with Sam Batdorf, whom Bernie came to regard as his most important mentor. Motivation for the new slip theory came from an extensive series of plastic buckling experiments on plates and shells at Langley and elsewhere that revealed that predictions from the so-called deformation theory of plasticity (in reality, not a plasticity model but a nonlinear elasticity material model) consistently did a better job reproducing experimental results than those from the most widely used, and supposedly more Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 19 BERNARD BUDIANSKY 41 physically acceptable, plasticity model. Budiansky’s slip theory clarified this paradox by showing that the widely used plasticity model predicted overly stiff responses under defor- mation responses typically encountered in buckling, while, in an approximate way, the deformation theory captured the less stiff response expected from a more sophisticated plasticity model based on crystalline slip. After his graduate years at Brown Bernie returned to NACA and in 1952 became head of the Structural Mechanics Branch. At Langley he met Nancy Cromer, a North Carolinian who assisted with large numerical computations before the era of electronic computers. The couple married in 1952 and had two sons, Michael and Stephen. Throughout the years that followed, Nancy balanced Bernie’s faux aggressive, New York style with an equally smart, calm humorous manner. The couple shared many interests, such as literature, good food, travel, and even horse racing. In 1955 Bernie accepted a position as associate profes- sor of structural mechanics at Harvard University, where he soon assumed the Gordon McKay Professorship in Structural Mechanics. He remained at Harvard for the rest of his career. Initially, he continued his groundbreaking research on struc- tures. One example is his work published in the early 1960s with a PhD student, N.C. Huang, on the nonaxisymmetric buckling of clamped spherical shell caps subject to pressure, an outstanding problem connected with reentry capsules. Their work demonstrated the utility to structural analysis of numerical methods executed by computers. Budiansky solved the nonlinear axisymmetric prebuckling problem, and the two men obtained the buckling pressure and mode by solving the nonaxisymmetric buckling problem. The results could not have been obtained without the aid of a computer. An open question in the late 1950s and well into the 1960s was the reason for the exceptionally large discrepancy between experimentally measured buckling loads of shell structures and predictions of buckling loads for these structures from shell theory. The two extreme examples are cylindrical shells under axial compression and spherical shells under external Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 19 42 MEMORIAL TRIBUTES pressure, both of which buckle at loads typically as low as a fourth or fifth of the theoretical prediction. Bernie appears to have been the first, other than W.T. Koiter himself, to appreci- ate that Koiter’s general theory of elastic stability and imper- fection sensitivity held the answer to the discrepancy. In 1945 in war-time Holland, Koiter developed and pub- lished (in Dutch) his thesis at Delft University, an elegant theory of elastic stability that laid out nonlinear buckling behavior and the sensitivity of buckling to initial structural imperfections. This theory revealed why experiments and classical buckling theory are in general agreement for columns and plates (they are not imperfection-sensitive) and why they are in sharp disagreement for many shells (they are extremely imperfection-sensitive). With the help of a colleague who could read a little Dutch, Bernie translated Koiter’s thesis into a mathematical form that in many ways was more transpar- ent than the original and thus introduced it to the American structures community. Then, with the assistance of a young colleague (the author of this memoir), he wrote a series of papers on the nonlinear behavior buckling of structures based on this approach, which had a transformative influence on elastic stability and set the stage for a rational way of dealing with imperfection-sensitive structures. During the same time period, and in parallel to his work on buckling, Bernie was one of the leading contributors to the development of the theory of shells. In this effort he collab- orated closely with a colleague at Harvard, J. Lyell Sanders. Their work was carried out in harmonious coordination with Koiter in Delft. In the early 1960s there were numerous competing sets of shell theory equations creating considerable confusion for engineering users. Koiter made a major breakthrough by showing that errors inherent to any two-dimensional theory of shells meant that many of the competing theories were equivalent as far as accuracy was concerned. Budiansky and Sanders followed up by identifying a theory that combined accuracy with additional desirable mathematical features. In their tongue-in-cheek title, they designated it “The Best Theory,” and it remains the standard. Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 19 BERNARD BUDIANSKY 43 Beginning in the 1960s, much of the research in solid mechanics shifted from structures to materials, and Bernie was one of the leaders in this transition. His earliest contri- butions used self-consistent averaging methods to compute the stress-strain behavior of polycrystalline materials based on the elastic-plastic response of the single crystal constitu- ents. With geophysicist Richard J. O’Connell he made a major contribution to the fundamental understanding of seismologi- cal wave speeds by applying these methods to determine the influence of microcracks, and the role of water infiltration into the cracks, on the effective elastic moduli of rocks. Many other contributions to what became known as micromechanics fol- lowed, including the role of fiber debonding and sliding in the tensile fracture of fiber-reinforced composites, fiber kink-