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 earthquakeproof
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 threedimensional 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 Lagrangiantype 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 byproduct 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 radioguidance 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 pulsegenerated 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
(193435), Louvain (193537), Columbia (193745), and Brown (194650)
Universities. During the war, as a Lieutenant Commander in the U.S.
Navy, he headed the Structural Dynamics section of the Bureau of Aeronautics
(194345). He wrote Mathematical Methods in
Engineering (with Theodore von Kármán, 1940),
Mechanics of Incremental Deformations
(1965), and Variational Principles in Heat
Transfer (1970).
