Maurice Anthony Biot

American engineer, physicist, and applied mathematician

Born May 25, 1905, Antwerp, Belgium

Manuscript Biot was working on minutes before his death.



The work and original contributions that distinguish Biot's career cover an unusually broad range of science and technology including applied mechanics, sound, heat, thermodynamics, aeronautics, geophysics, and electromagnetism. The level of his work has ranged from the highly theoretical and mathematical to practical applications and patented inventions.

His pioneering work in the 1930s on the response of structures to transient disturbances led to the key concept of response spectrum as a universally applied tool in earthquake-proof design and in many other problems. It is during the same period that he published his first papers on a new approach to the nonlinear theory of elasticity accounting for the effect of initial stress.

Aeronautical problems and fluid mechanics were the object of most of his effort during the 1940s. He developed the three-dimensional aerodynamic theory of oscillating airfoils along with new methods of vibration analysis based on matrix theory and generalized coordinates. This led to widely applied design procedures of complex aircraft structure in order to prevent catastrophic flutter. He also patented an electrical analogue flutter predictor based on a simple circuit design which simulates aerodynamic forces. After the war he continued to work on nonstationary aerodynamics and aeroelasticity including the divergence instability of thin supersonic wings, and the first evaluation of the transonic drag of an accelerated body. In the 1950s Biot's work was concerned primarily with problems of solid mechanics, porous media, thermodynamics, and heat transfer. He developed a new approach to the thermodynamics of irreversible processes by introducing a generalized form of the free energy as a key potential. The formulation was associated with new variational principles and Lagrangian-type equations. The results with the introduction of internal coordinates provided the thermodynamic foundation of a completely general theory of anisotropic viscoelasticity and thermoelasticity. As a by-product of this work, Biot developed a new approach to heat transfer based on generalized coordinates and a Lagrangian system analysis, which shows remarkable accuracy and avoids some physical inconsistencies of traditional methods. He later gave a systematic presentation of this work in a monograph published in 1970 and indicated its applicability to many other problems such as those of aquifers or neutron diffusion in nuclear reactor design.

Biot's interest in the mechanics of porous media dated back to 1940 with a fundamental paper in soil mechanics and consolidation. He returned to the subject in the 1950s in the more general context of rock mechanics in connection with problems in the oil industry. On the basis of his earlier work in thermodynamics he published a large number of papers which provide a completely general and systematic theory of porous solids containing a viscous fluid. He showed that in such media there exist three types of acoustic waves.

For a short period in the middle 1950s Biot became involved with rocket radio-guidance problems and the question of disturbance from ground reflections. To evaluate this effect he developed an original theory for the reflection of electromagnetic and acoustic waves from a rough surface, showing that the effect of the roughness may be replaced by a smooth boundary condition. At the same time in collaboration with Ivan Tolstoy he introduced a new approach to pulse-generated transient waves based on a continuous spectrum of normal coordinates. The combination of the two methods provides the only practical solution to some important problems.

In a series of papers starting in 1957 Biot extended his earlier work in the mechanics of initially stressed solids, developing a mathematical theory of folding instability of stratified viscous and viscoelastic solids. He verified the results in the laboratory and applied them with considerable success to explain the dominant features of geological structures. The results were also found to be consistent with the geological time scale. In particular he brought to light the phenomenon of internal buckling of a confined anisotropic or stratified medium under compressive stress and provided a quantitative analysis. He applied the theory with the same success to problems of gravity instability and salt dome formation. In a later period he presented a systematic treatment of the mechanics of initially stressed continua in a monograph published in 1965. On the basis of these results in the theory of stratified media Biot also derives a new approach to the analysis of engineering structures which involves multilayered plates and composite materials. He derived the characteristic stress distribution features of strongly anisotropic material, which are significant from an engineering standpoint.

In the 1970s Biot's formulation of his Variational Principle of Virtual Dissipation in the thermodynamics of irreversible processes, along with a new approach to open systems, represents contributions which are fundamental and far reaching. The principle leads to a synthesis of classical mechanics and irreversible thermodynamics. At the same time he originated new concepts in the thermodynamics of open systems which eliminate the traditional difficulties inherent in Gibbs' classical theory. As a consequence he derived a new chemical thermodynamics, leading to the concept of intrinsic heat of reaction which provides an improved measure of the true chemical energy, as well as new expressions for the affinity and heat of reaction. He has applied these new theories to obtain directly the field equations in systems where deformations are coupled to thermomolecular diffusion and chemical reaction. On this basis he also developed further the theory of porous media including heat and mass transfer, with phase changes and adsorption effects.

Biot graduated from the University of Louvain with a bachelor's in Thomistic philosophy (1927), mining engineering (1929), electrical engineering (1930), and Doctor of Science (1931). He received a doctorate in aeronautical sciences from the California Institute of Technology in 1932. He held teaching positions at Harvard (1934-35), Louvain (1935-37), Columbia (1937-45), and Brown (1946-50) Universities. During the war, as a Lieutenant Commander in the U.S. Navy, he headed the Structural Dynamics section of the Bureau of Aeronautics (1943-45). He wrote Mathematical Methods in Engineering (with Theodore von Kármán, 1940), Mechanics of Incremental Deformations (1965), and Variational Principles in Heat Transfer (1970).