Biography

He obtained degrees in electrical engineering, mining engineering, philosophy as well as a D. Sc. (1931) at the University of Louvain.

He went to Caltech where he received a Ph. D. (1932) in Aeronautical Sciences and was first a student and then a collaborator of Th. von Karman, with whom he wrote a classic textbook,Mathematical Methods in Engineering.

He taught at Louvain, Harvard, Columbia where he taught theoretical mechanics. This was interrupted in 1940 while he took leave from Columbia University to assume responsabilities for research and teaching in aeroelasticity at Caltech (O.SRD)

As Lt. Cmdr. U.S. Navy, he was Head Structural Dynamics Section, Bureau of Aeronautics and member Naval Tech. Mission in Europe.

After the war he was, briefly, on the faculty of Brown University.

He became an independant scientific consultant working for Shell Development, Cornell Aeronautic Lab., sundry government agencies and Mobil Research.

As an applied mathematician and physicist, his work and original contribution cover an unusually broad range of science and technology including elasticity theory, soil mechanics, waves propagation and scatter, wing flutter, geophysics, seismology, thermodynamics, etc.

His pioneering work on the response of structures to transient disturbances led to the key concept of Response Spectrum Method as a universally applied tool in earthquake proof design.

During the 1940's he developed a three dimensional theory of aircraft flutter and introduced matrix methods and generalized coordinates in aeroelasticity. This led to widely applied design procedures of aircraft structures in order to prevent catastrophic flutter.

His interest in the mechanics of porous media dates back to 1940 with a fundamental paper in soil mechanics and consolidation. He returned to the subject in the more general context of rock mechanics.

His theory of wave propagation in fluid satured porous elastic solids has proved enormously valuable in describing quantitatively the damping of ocean sound waves interacting with bottom sediments.

His elegant theory of non linear elasticity accounting for the effect of initial stress culminated in 1965 in a monograph entitled Mechanics of Incremental Deformation.

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.

In collaboration with Ivan Tolstoy he introduced a new approach to pulse generated transient waves based on a continuous spectrum of normal coordinates.

He developed a mathematical theory of folding instability of stratified viscous and viscoelastic solids and applied the results to explain the dominant features of geological structures. He brought to light the phenomenon of internal buckling of a confined anisotropic or stratified medium under compressive stress and provided a quantitative analysis.

The formulation of his variational principle of virtual dissipation in the thermodynamics of irreversible processes along with a new approach to open systems represent contributions which are fundamental and far reaching. The principle leads to a synthesis of classical mechanics and irreversible thermodynamics.

He also originated new concepts in the thermodynamics of open systems which eliminate the 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 and improved measure of the true chemical energy, as well as new expressions for the affinity and heat to reaction. He applied these new theories to obtain directly the field equations in systems where deformations are coupled to thermomolecular diffusion and chemical reactions. On this basis he also developed further the theory of porous media including heat and mass transport with phase changes and absorption effect.

 

 

BIOT published 179 articles and was the holder of 7 patents.

He wrote Mathematical Methods in Engineering (with Th. von Karman), Mc Graw Hill, 1940).

Mechanics of incremental Deformations, Wiley, (1965),

Variational Principles in Heat Transfer, Oxford, (1970).

Unusual was his ability to produce so much first-rate research while working without students and essentially alone.

He contributed new techniques and created original concepts.

 

Complete list of publications

 

 

Outline of contributions

1928

During his studies he published his first article: Hydrodynamique Moderne et
Aeronautique (5 - 11)

1929

He patented The Radioguidance System for Ship and Aircraft published later (4)

1931-33

With support of the Belgian American Educational Foundation, he spent 2 years at CALTECH where he received a PhD in Aeronautical Sciences (June 1932 - thesis 259). It has become his pioneering work on Response Spectrum Method (RSM) as a universally applied tool on earthquake proof design (chap 2 of his thesis). A complete outline of this work has been given in 2 publications (10 - 20) later he published “Mechanical Analyzer for prediction of Earthquake Stresses” (41) and “Analytical and Experimental Methods in Engineering Seismology” (45)

1933

He spent a summer session at the University of Michigan where he was taught the theory of Solid Mechanics by the great Stephen Timoshenko.

1934

Back to Europe he visited Delff, Zurich, Cambridge Göttingen universities.

1934-35

Instructorship at Harvard (Graduate School of Engineering) (21 – 24 – 25 – 26 – 27 - 29)

1936

University of Louvain: he taught Analytical Dynamics and theory of Elasticity

1937

Columbia University: Institute of Physics – he taught analytical dynamics, elasticity, hydrodynamics, vibrations theory, aerodynamics, etc.

He went back to the nonlinear theory of elasticity accounting for the effect of initial stress and large rotation. This basic theory was first published between 1937-1940 in seven papers (17 – 31 – 32 - 33 – 34 – 36 – 38) (interrupted by the war).

In 1965 his important book Mechanics of Incremental Deformations explained, with many other new fields along with the theory of Electricity.

1937-40

He achieved the text book (began in 1932 at Caltech in collaboration with Theodore von Karman: Mathematical Methods in Engineering published in 1940. Later translated in 9 languages.

1940

On leave of absence from Columbia – called at the request of Dr.R. Millikan to contribute his special knowledge of vibrations problems, he jointed Caltech as research associate in charge of teaching and research in aeroelasticity. He developed many important publications reports OSRD and GALCIT. Many of great importance during WW2.

1941

U.S.naturalized

1942

Enlisted in the U.S.Navy (Researches and teaching at Caltech under OSRD)

1943-45

Volunteer ALSOS in European théatre of operations, joined the Combined Allied Forces Task) and CIOS (Combined Intelligence Objective Sub-Committee) gathering scientific intelligence on aircraft and missiles in Germany. (Some are readable now on the Web).

1946-52

After the war: Brown University: Graduate division of Applied Mathematics. Professor of Applied Physical Sciences.

1947-48

He continued work on aeroelasticity including the Divergence Instability on thin supersonic wings and the first evaluation of the transonic-drag on an accelerated body (48 – 49 – 50 – 51-59-71) (Reports Cornell Aeronautic Lab (1 to 6)

Poroelasticity

The Biot theory of Poroelasticity is a great contribution to geophysical and acoustical fields. It held to the key of understanding and interpreting a mass of wave attenuation and propagation data in seismic, ocean sediment, geophysical well logging, consolidation, mechanics, biomechanics...

His fundamental paper (40) was developed while he was member of the Physics Department of
Columbia. He returned to the subject in the more general context of rock mechanics.

On the basis of his earlier works on 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 exist three types of acoustic waves.

The theory proved enormously valuable in describing quantitatively the damping of ocean
bottom sediments.

He has intended to write a monograph on the subject covering the period 1941-1978, with a connecting text and an appendix. He selected 21 of his papers.
Alas he did not live to finish this plan.

Ivan Tolstoy edited these 21 papers in a volume published i 1992 by the Acoustical Society and
the American Institute of Physics, entitled 21 papers by M.A.Biot:

Nrs 23 – 40 – 42 – 43 -44 – 55 – 57 – 60 – 61 – 63 – 68 - 97 – 98 – 99 – 109- 118-
139 – 142 – 150- 155 – 157 – 160 – 161 -

In 1996, Alexander Cheng founded the Poronet internet resources network: A Tribute to Maurice Anthony Biot.

In 1998 a Biot Conference on Poromechanics was organized in Louvain-la-Neuve. (Belgium)

In 2002 a second in Grenoble. (France)

In 2005 (100th anniversary of Biot's birth) the Conference was held in Norman (Okl.)

The fourth in New York in 2009.

The fifth in Vienna in 2013.

The sixth is already programmed in Paris in 2017.

1957

Rocket radioguidance problems and question of disturbance ground reflection.
He developed an original theory for the reflection of electromagnetic and acoustic waves from a rough surface showing that the effect of roughness may be replaced by a smooth boundary condition. (74 – 75 – 77 – 78 – 136 - 141) Nrs.136 and 141 lay the foundation of the original theory of rough surface scatter which has been generalized in applied acoustics. At the same time, in collaboration with Ivan Tolstoy, they introduced approach to pulse generated transient waves based on a continuous spectrum coordinate (70). The combination of the two methods provides the only practical solution of some important problems.

1957-1967

General theory of Folding Instability of Stratified Viscous and viscoelastic Solids
  This development has open a new phase in geology. It was initiated in 1948 as a systematic program. The results are embodied in a series of papers published since 1957:
  72  – 81 – 83 – 84 – 85 – 90 – 91 – 92 – 102 – 110 -116 – 117 - 118  - 119 – 120 – 124 – 125 – 128 – 132 – 135 – 137 – 138 – 140

  He verified the results in the Laboratory and applied them to explain the dominant features of geological structures; the results were also found to be consistent with geological time scale. 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: 79 – 87 – 111 -126 -130

  On the basis of the results in the theory of stratified media he derived a new approach to the analysis of engineering structures which involve multilayered plates and composite materials.  He derived the characteristic stress distribution feature of strongly anisotropic materials which are significant for engineering standpoint.

  In a later period he presented a systematic treatment of the mechanics of initially stressed continua in a monograph « Mechanics of Incremental Deformation” (Wiley, 1965)

a) Important steps and distinct phases in the Theory of Folding

The initial phase deals with the single layer and the concept of dominant wavelength. This work was done during the years 1950-1960 and published starting in 1957 (72) . In order to prepare its appli-cation to Geophysics, (mountain formation) gravity was introduced for the case of a layer on an infinite medium of decreasing viscosity with depth. Results for the last two cases indicated the im-portance of multilayers to explain large scale folding. The assumption of thin layer theory without adherence was checked by treating the layer as a continuum and also evaluating separately the ef-fect of adherence.
The next step was to evaluate the geological relevance of the results quantitatively, and to verify the theory experimentally. This was started around 1960 (90, 91, etc.). Using currently accepted values of rock viscosities, it was found that the time required for folding fitted the geological time scale.
An important theoretical analysis predicted how the dominant wavelength emerges from a bell shaped disturbance from the flatness and is pratically independent of the sharpness of the disturb-ance.
The increase in layer thickness tends to compensate the shortening thus maintaining the magnitude of the dominant wavelength as predicted by the simple theory.
The subsequent phase dealt with multilayers. This was first discussed in (90) in the geophysical con-text. Exact more elaborate theories for multilayers and laminated anisatropic media were then de-veloped for viscous elastic and viscoelastic materials.
In 1964 an important step was the development of a theory rigorously applicable to stratified « Newtonian fluid undergoing finite compressive strain » (120, 126).
The important gravity analogy was brought out replacing gravity by surface and interfacial forces.
In 1964-65 the folding of confined multilayers was shawn to be derived from the concept of inter-nal buckling and the existence of a dominant wavelength was brought out. The essential features are embodied in a simple formula explaining a prevalent aspect of geological folds as related to their thickness and the confinement geometry.
In 1965 two types of folding for a surface multilayer were brought out and characterized by a « transition wavelength ».
Pure gravity instability was treated in the context of salt dome of formation applying the gravity analogy method. Significant parameters were brought out, and the theory was applied to an over-burden of variable thickness (127).
It was shown to be directly applicable to three dimensional problems (130).
In 1967 a couple stress analogy was developed extending the theory to multilayers with individual layer being themselves composed of thinly laminated media. This points to simultaneous appearance of dominant wavelength of different magnitude (132).
In 1968 folding with non sinusiodal spatially attenuated waves was derived (135) as may exist near an edge or a fault.
Finally in 1974, a complete theory was developed for laminated media and multilayer for compress-ible material with a very general type of initial stress including shear.
Attention is called to a skin effect in bending of multilayers. Attention should also be called to in-terstitial flaw connection for internal buckling (128) and to the property of non-oscillatory instabil-ity.

b) Outline of developments on Folding Instability
Initial paper (72) treated the general case of a layer as a thin plate for viscoelastic media, with purely viscous media as a particular case. In the viscoelastic case thermodynamic principles have an important bearing on the behavior. Concept of dominant wavelength.
The same theory based on the continuum theory instead of plate theory was treated for both non-adhesing layer (81) and adhesing layer (92). The adhesing layer based on plate theory was also analysed (83).
A survey of results and some preliminary experimental work is found (84 - 85) along with results for the effect of gravity and the case of continuous inhomogeneity. The influence of gravity was analysed in detail for the homogeneous layer (79) and the continuously in homogeneous case.
At this point experimental verification was needed through lab test as well as a confronta-tion of the theory with geological data and time scales. This was done in (90) and (91). This also included an analysis of the development of folds from an initial layer disturbance, showing the validity of the concept of dominant wavelength.
The theory of folding was found to be verified experimentally and relevant geologically.
A preliminary discussion was also given for the case of multilayers. The concept of wave-length selectivity was introduced. Attention was called to the phenomenon of internal buckling of a confined medium (102). This constitutes one of the important features of confined multilayers. Exact theories of stability were developed for multilayered continua 110 -111-115 - 116 - 117. The case of folding of a porous layer was analyzed 118.
A theory of folding of multilayers based on a rigorous application of the Navier Stokes equation was developed in 120. The fluid undergoes finite strain as a function of time and an in-stable small perturbation is superposed.
A geologically important result is obtained in 119 and 128, when the internal buckling are considered of confined multilayers. Simple formula are derived for the folding wavelength which explain an important feature of geological structures.
Internal instability of a confined anisotropic viscoelastic continuum is analyzed in 124.

In 128 folding of multilayers under gravity is consider. The concept of transition wavelength is brought out, this separating the region when the folding is an overall bending, and the region when it is mainly shear.

In 126 folding with finite strain is considered and it is shown how a pinch effect (concentric folds) must be expected. Exact fluid mechanics is also applied to the single embedded layer and compared to plate theory. A gravity analogy is derived applicable to the effect of gravity. Gravity instability applicable to salt domes is treated in 127 - 130 in two and three dimension including a variable thickness of the overburden due to gradual sedimentation.
In 132 a more rigorous theory is developed for internal buckling of laminated media, and multi-layers, which may be homogeneous for each layer or laminated.
A couple-stress analogy is developed.
Some folds of different wavelength may develop simultaneous since the corresponding amplifica-tion factors may be about the same.
The folding which dies out away from a fold is treated in 135.
An elaborate theory of laminated continua is developed in 144.
Initial stresses may include normal and shear stresses.

Exact and simplified approaches are considered for plates which are multilayered composites.


 As often heard, Tony had a unique mastery of variational principles, the used of which he extended to new domains such as finite elasticity, poroelasticity, heat transfer, thermodynamics, etc…
(As we have seen later…)

1954

Thermodynamics of Irreversible Process:

In the middle of 1950 (first paper) (54) he developed a new approach to the Thermodynamics of irreversible process by introducing a generalized form of the free energy as a key potential. The formulation was associated with new variational principles and Lagrangian type equation.

The result with the introduction of internal coordinates provided the thermodynamics foundation of a completely general theory of anisotropic viscoelasticity and thermoelasticity.

As a by product of this work he developed a new approach to heat transfer based on generalized coordinates and a Lagrangian systems analysis, which shows remarkable
 accuracy and avoids some physical inconsistencies of traditional methods.

He published a large number of papers: 54 – 56 – 58 – 62 – 65 – 66 – 73 – 76 – 80 – 82 – 88 – 93 – 94 – 95 – 96 – 99 – 109 – 121 – 122 – 129 – 133 - 134
 
 He later gave a systematic presentation of this work in a monograph:

1970

“Variational Principles in Heat Transfer”
 
 A unified Lagrangian analysis of Dissipative Phenomenom,
 (Oxford University Press, 1970)

And indicated his applicability to many other problems such as those of aquifer, neutron, diffusion in nuclear reactor design, electromagnetic, porolesasticity, thermodynamics,etc (in an important appendix)

N.B. papers 54 – 56 – 62 – introduced the Langrangian methods which were to be the hallmarks of most other domains.
 
 N.B. MRS BIOT FOUND THIS NOTE AFTER HER HUSBAND. DEAD
 
  A new revolutionary development in Thermodynamics has recently been initiated.
It embodies a twofold aspects. One is represented by a new principle of virtual dissipation which generalized the classical d’Alembert’s principle of mechanics to completely general non-linear irreversible thermodynamic.

 The other is provided by an entirely new approach to the thermodynamics of open systems which introduces a new concept: the “Thermobaric Potential” leading to the new definition of the chemical potential and avoids Gibbs paradox without recours to Nesset’s principle or statistical mechanics.

  Areas of application either potential or already initiated are indicated as follows.

 A unified thermorehology of solids and fluids has been developed. The atmospheric dynamics or the biomedical problems of flow of body fuids.

 A unified thermodynamic approach to the dynamics of fluid mixtures with thermomolecular diffusion and mutual and self viscosities has also been developed. The method is entirely new and uses to the new concept of termobaric potential, which provides a powerful method of dealing with coupled flows of heat and matter. A particularly interesting aspect of the new approach, in addition to its improved generality over of the present results, is the possibility of taking into account vapour properties and phase changes.

 A large area of application is the theory of coupled deformations, fluid and thermal flow, in porous solids including phase changes.
 This includes the analysis of heat pipes and the systems analysis of heat pipes and the systems analysis of large complex geothermal systems for power production.

 The concept of thermobaric potentials also leads to a revolutionary approach to chemical thermodynamics. Enormous simplification of the thermodynamic treatment is achieved and new results have been obtained which are more general than those available in the classical literature. By incorporating these result in the fluid mechanics a potentially new and powerful approach is obtained for the analysis of combustion and shock waves including relaxation and diffusion effects.

 Potentials applications should also be mentioned in plasma physics, and radiation problems. This includes stability non equilibrium problems. The analysis of pulsating stars could be attacked in novel fashion.

 In both method and spirit the program constitutes a basic departure from those of present schools. From a purely mathematical viewpoint it avoids formalistic and  non elementary method while achieving results which go for beyond current developments.

 In particular unified functional space concepts are used implicitly without recourses to existing ponderous definitions and method, using new and elementary procedures, based on the concept of resolution threshold.

1975

New thermodynamics. (Variational Lagrangian reformulation of irreversible process)

 In the 1975 he derived a new chemical thermodynamics, leading to the concept of intrinsic heat of reaction which provides and improved measure of the true chemical energy, as well as new expressions for the affinity and heat of reaction. He has applied these news theories to obtain directly the field equations in systems where deformations are coupled to thermos molecular diffusion and chemical reactions.

 On this basis he also extended further in the theory of porous media including heat and mass transport with phase changes and absorption effects. (150 – 155 – 157 – 160 – 161)

 The principles lead to a synthesis of classical mechanics and irreversible thermodynamics.

1984

In 1984, he wrote a survey article which can be seen as a generalized and unified presentation of most of his previous work prestressed solid mechanics, poroelasticity and thermodynamics.