A version of this essay including photos and the French original is available in PDF.

Huy Duong Bui, member of the French Academy of Sciences, passed away on May 29, 2013 at the age of 76. He was a founding member of the French Academy of Technologies, a member of the European Academy of Sciences and a Fellow of the Institute of Physics (London). He was also a Knight in the French Ordre national de la Légion d'honneur.

Huy Duong Bui was born in Hanoi on March 16, 1937. As a child in Vietnam, he had been kept away from town and deprived of schooling for a long time because of harsh years of wars, floods and famine: a refugee in the countryside with his family, he learned hunting and fishing from his father; he also learned to gaze at the stars and, above all, he developed the practical turn of mind, manual skill, intellectual curiosity and ingenuity which would mark his personality. His paternal grandfather, an educated man, gave him an appetite for studying and taught him the basics in Vietnamese and arithmetic. But, having been deprived of schooling up to the age of 12, he failed the entrance exam to the French Lycée of Hanoi because his French was not good enough. Thus, Bui (as we used to call him) attended a private school for three years and then spent two more years as a self-educated young man, which resulted in an easy success at the Baccalauréat exam in 1955. Because he was noticed as a student of exceptional intelligence he was awarded one of the few scholarships to study in France in the preparatory classes for the Grandes Écoles. So he entered the “Math Sup” class of Professor Jean Itard (otherwise well-known as a historian of mathematics) in Lycée Henri IV (Paris), almost one quarter late due to administrative delays. After one more quarter, he had made up for this handicap and, after one year of “Math Spe”, he entered the École Polytechnique in 1957. He graduated in 1959 and then entered the École Nationale Supérieure des Mines of Paris for a two-year specialised program. Bui's scientific career would then begin.

In a biographical text which he regularly updated until a few months before he died, Bui good-humouredly reveals that it was his failure to pass the “little psychotechnical tests, really just disjointed children's games” that were then much in vogue, during an IBM hiring interview, which led him in December 1961 to the Solid Mechanics Laboratory at the École Polytechnique, which Professor Jean Mandel had just founded.

Bui's admission to this nascent laboratory was not without practical difficulties, but they were eventually solved with his hiring by the electric utility company Électricité de France (EDF) to perform studies in solid mechanics relevant to nuclear power plants, then still in the planning stages. In fact, Bui's scientific career is intimately tied to this laboratory, where he remained throughout his life in various administrative positions. This unusual situation, maintained thanks to the far-sightedness of successive directors of EDF Direction des Études et Recherches (DER), largely explains the nature of Bui's scientific work, which was motivated, if not guided, by the research needs of the French energy supply programme.

Apart from its extent and consistency, Bui's scientific work has been characterised from the beginning by its elegance and subtlety. It falls squarely within the mechanics of deformable solids, but not without incursions into fluid mechanics when necessary for the analysis of coupled problems. His scientific contributions can be grouped into four main fields: mechanics of materials, fracture mechanics, numerical methods with a special emphasis on boundary integral equations, and inverse and identification problems. This classification will serve as a useful guide in this outline, although it tends to hide the logical and chronological development and interconnected of Bui's interests, which blends results he obtained in all these different fields.

Mechanics of materials

Bui's PhD thesis, defended in 1969, dealt with the elastoplastic behaviour of metals. Motivated by the research programme linked to the Mediterranean gas pipeline, it contains in embryo several topics in which Bui was later to excel. First, it was an experimental study which Bui designed and performed personally: starting from the initial boundary of the elastic domain he established the work-hardening evolution of the yield surface according to the incremental load applied to the specimen. For this, Bui devised and carried out combined tension-compression and torsion tests on aluminium, iron and copper thin tubes; he introduced disruptive metrological advances which allowed him to gain at least one order of magnitude on the permanent strain offset. This point constituted an essential breakthrough; it must be well understood that the boundary of the elastic domain in a given work-hardening state can only be determined from the detection of new permanent strains observed along various loading paths, and that these new permanent strains themselves modify the hardening state at the same time! In particular, the results obtained, which were completely novel and are now referred to as seminal, showed an unexpected behaviour during the early stages of work-hardening which was contrary to the Bauschinger effect. They also allowed the investigation of the influence of the loading path, the occurrence of corners on the yield surface and the relevance of the “normality rule”. Moreover Bui developed in his thesis a theoretical analysis in the same spirit as Hill and Mandel: through a pioneer approach of “homogenisation of random media” he made up a physical model which could explain the overall elastoplastic behaviour of the metallic polycrystal he had investigated experimentally, from the single crystal behaviour.

At the end of the 70s, Bui resumed working in mechanics of materials under the pressure of the research programme on the constitutive equations of steels used in the EDF power plants, with a special interest in the critical aspects of damaging and fracture and in the “micro-macro” relationships. Then, during the 90s, he became interested in the micromechanics of solid surfaces, the discontinuity interfaces of materials — such as welds — or load discontinuities — such as thermal shocks. Concerning this latter topic, he brought to light the (very localised, bounded, discontinuous, with an unbounded gradient) stress singularity he named “the thorn singularity”; this concept made it possible to explain observed superficial damaging phenomena, such as thermal crazing, and constituted an advance, followed by others, towards the control of superficial damaging phenomena of materials.

To finish with this topic, which has essential industrial applications, it is worth mentioning that Bui made important technical contributions by putting his scientific expertise to use in helping to draft the building code for the construction of fast neutron nuclear power plants. He was also involved, as the EDF project manager, in the Brite-Euram contract on fibre-reinforced concrete, a subject motivated by the early damages observed on some cooling towers. Bui also took part in the investigation of mechanical and rheological problems posed by the underground storage of radioactive waste; his skills in combining theory, numerical computations and in situ tests proved very useful in that research.

Fracture mechanics

Bui got interested in fracture mechanics soon after his thesis. Following the main trend of research at that time, he devoted himself to the characterisation of singularities at the crack tip in order to derive the stress intensity factors, a key tool in brittle fracture mechanics:

• He stated a conservation law dual to that established by Eshelby in 1956.
• He constructed the invariant integral $I$ dual to the $J$ integral of Rice and Cherepanov, so as to make it possible to get numerical upper and lower bounds of their common value.
• He constructed two invariant integrals which allowed him to separate fracture modes I and II in the $J$ integral (these results were implemented in CEA and EDF computer code).
• With a view toward applications to thermoelastic fracture mechanics, he established a method for the construction of a “divergence-free” conservation law for problems that naturally exhibit a source term, which makes the accurate computation of singularities easier.

Together with Amestoy and Dang Van, using multiple-scale techniques and matched asymptotic expansions, Bui gave an analytical solution to the problem of a bifurcated crack, which had only been treated numerically before; later he completed this result with Amestoy and Leblond for the case of a curved bifurcated branch. With Ehrlacher and Nguyen, he stated the logarithmic singularity of the temperature field due to the point heat source which appears at the tip of a crack propagating in an elastic solid — a result that conformed with the experimental evidence then available, which he confirmed through his own experiments. The introduction of a decohesion law with a threshold in the constitutive equations of an elastic material allowed Bui and Ehrlacher to derive analytical solutions to the quasistatic and dynamic crack propagation problems in mode III (mathematical problem of a free boundary between the damaged zone and the still elastic zone) and, incidentally, to solve Rice's paradox in the theory of ductile fracture for a perfectly plastic material.

To investigate dynamic fracture, Bui originated what is called the compact compression specimen (also known as the “clothes peg” specimen), which proved itself a remarkably effective tool of experimental analysis, and he used it in the study of the leakage flow rate through cracks. So, he was led to study various aspects of fluid-crack interactions taking surface tension into account, especially for nuclear power plant safety. Let us briefly quote the results he obtained in the field of hydraulic fracturing: a model of two-dimensional flow of a viscous fluid at the tip of a motionless crack, which can remove the pressure singularity induced by classical modelling; a model of the interaction for a propagating crack introducing the capillary tension and assuming void formation between the fluid convex meniscus and the crack tip: the coupled problem was solved numerically and brought the flow two-dimensional structure to light. Bui was recognised as an expert for these problems which now have numerous industrial applications.

Bui was one of the world leaders in the field of brittle fracture mechanics. The book he published in 1978 is still authoritative today.

Boundary integral equation methods

This topic is obviously closely connected to the preceding ones. First, Bui noticed some anomalies in the numerical results obtained in thermo-elastoplasticity; reconsidering the integral equations currently used by researchers and engineers, he showed that the corresponding integral kernel was not complete, and restored the exact equations by adding a point distribution. Later on, he investigated this field again; he tackled dynamic problems and, with Bonnet and Loret, he exhibited a very simple regularisation method for the singular elastodynamics integral equations, which led to higher accuracy in its numerical implementation. This method has been used, among others, by Madariaga (IPG, Institute of Earth Physics of Paris) and Bonnet in a paper published in Wave Motion in 1991. In a later paper, Bui proposed a nonsingular variational method which saves symmetry and yields an a posteriori error indicator.

Inverse problems and identification

On this fourth main topic, Bui published the book Inverse problems in the mechanics of materials: an introduction in 1993. It has been translated from French into, among other languages, English, Japanese, Chinese and Russian. Paul Germain, who wrote the preface to the French original, called it a “tour de force”: “The ability to fully expound in under 230 pages such a difficult body of knowledge can only be the result of wide and deep learning ... that feeds a thought process involving the constant reworking of acquired knowledge; it is also founded, crucially, on personal experience of the applications and methods exposed in this book”. Indeed, Bui did not lack personal experience in this field, but it is mainly his geometrical mind, rich with the notions of duality, symmetry and reciprocity, that inspired his dazzling intuitions and his singularly elegant treatments; at the same time, his mathematical ability allowed him to find disconcertingly simple analytical solutions to problems where so many others rushed in with numerical approaches. Thus, he was able to solve many problems related to crack, fault or matter lack detection or the reconstruction of load paths. A few examples:

• a direct analytical derivation of the dynamic stress intensity factor from the experimental measurement of forces and velocities applied at the surface, by solving a convolution equation (Bui and Maigre);
• the partition of kinetic, elastic and dissipated energies in a problem of crack propagation when the applied force, associated velocity, and crack length and opening are known experimentally;
• the identification of the elastic moduli tensor field in an inhomogeneous solid body from just measurements of forces and displacements at the boundary. Up to then, the available results only concerned the isotropic material and Bui showed that the identification was possible up to 6 elastic constants.

It was once more at EDF's instigation that Bui got involved in the study of the inversion of microgravity data which were measured on the Pyramid of Cheops: he diagnosed the presence of hollow internal spirals which, several years later, could be related to the construction theory with spiral internal ramps proposed by the architects Henri and Jean-Pierre Houdin.

Bui trained a great many young researchers and engineers. He succeeded in passing on not only his scientific knowledge and know-how but also his enthusiasm for research and passion for bringing together science and industry, theory and experiments, and basic and applied research. EDF is in his debt not only for his contribution to the development of the Mechanics and Numerical Models Department and the LaMSiD, a mixed EDF-CNRS research unit, and for his scientific expertise and penetrating analyses of scientific and technological progress, but above all for the exceptional human contingent that he built up through his research on the key problems of nuclear industry. The author of more than 100 papers and 4 books, some of which were translated into 7 languages, he not only helped advance the state of the art on most of the great topics in solid mechanics of the last fifty years, but also made a major contribution to the expansion of nuclear technology and to the success of the French nuclear industry.

His scientific portrait would not be complete if his personality were not evoked too, a personality made of discretion and scientific curiosity, of reserve and human warmth, of enthusiasm and modesty, of understanding and compassion towards others. This is unanimously attested to not only by his co-workers, researchers, students, engineers, technicians and administrative people, but also by a number of doctoral students under the guidance of other advisors who knew that his office door was always open when they needed scientific advice or comfort amid difficulties. This is also true for his fellow doctoral students in the Laboratory of Mechanics, including the undersigned, who, to various degrees, have benefited from his interest and advice, suggestions or recommendations, concerning theory, bibliography, experiments or methodology.

Georges Charpak bestowed nobility on the word “handyman”: in this sense, we can qualify Bui as a “handyman of genius” as well as an outstanding theoretician. We all retain Bui's memory as a figure who radiated intelligence and inventiveness as well as kindness and generosity.

Bui had been suffering for a long time from asthma, which gradually made his voice fainter and fainter, but he died of a serious disease which was only diagnosed in November 2012. He accepted this illness not with resignation but with philosophy; shortly before he died, he wrote to his dearest and nearest: “For me, death is the continuation of life in another form.” He passed away with serenity and confidence.

In the conclusion of the 2013 edition of his memoirs, which he gathered under the title “Schrödinger's cat in quantum mechanics and its double in solid mechanics”, he thanked all his co-workers and the personalities who helped him for the progress of his career and he wrote this especially touching dedication:

To the memory of my father and my mother; she was lost with so many other “boat people” in the China Sea.

Following his wishes, his own ashes were scattered in that same China Sea.

Jean Salençon and André Zaoui
October 2014

Milestones

Authors