Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Aero, Eron Lyuttovich

  • Victor A. EremeyevEmail author
  • Alexey V. Porubov
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_27-1


Cosserat Continuum Kuvshinskii Viscous Micropolar Fluid Account Rotational Inertia Micropolar Solids 
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Aero, Eron Lyuttovich (*May 14, 1934, village Naryshkino (Penza district), Russia, † July, 11, 2016, St. Petersburg, Russia) the scientist who made an outstanding contribution to the development of the mechanics of generalized continua such as Cosserat continuum and liquid crystals (Fig.1).
Fig. 1


Education and Carrier

Eron Aero graduated from the Radio-Technical Faculty (now Institute of Physics, Nanotechnology and Telecommunications) of the Leningrad Polytechnical Institute (nowadays known as Peter the Great St. Petersburg Polytechnic University) in 1959. He got the degree of Candidate of Sciences (Ph.D.) in 1975. In 1982 he received the degree of Doctor of Sciences for the dissertation entitled “Hydrodynamical theory of liquid crystals.” From 1960 to 1986, he worked at the Institute of Macromolecular Compounds of the Academy of Sciences of the USSR. From 1986 to 2016, he worked as the head of the laboratory of Micromechanics of Materials in the Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg.

Scientific Results

The first papers of Aero and Kuvshinskii on the model of the Cosserat continuum that appeared in the early 1960s (see Aero and Kuvshinskii (1961) and also Kuvshinskii and Aero (1964)) immediately were marked by such an outstanding scientist in the field of generalized continua as A.C. Eringen (1966a, 1967). They became pioneering works and gave rise to many studies in the field of micropolar mechanics; see Stojanović (1969a,b) for the state of the art at that time. The main finding was the obtaining of the potential and the material relationships invariant to the rigid rotation. Previous models were not invariant.

E. Aero was very active throughout whole his life. For example, he delivered the lecture on his recent findings in generalized continua at the Euromech Colloquium 510: Mechanics of Generalized Continua: A hundred years after the Cosserats (Maugin and Metrikine, 2010) in Paris just at the day of his 75th birthday. His outstanding contribution is widely noted in the literature; see, for example, Maugin (2013), page 184:

One is Eron L. Aero (born 1934) who, before even Palmov and long before anybody in the USA, produced (1960) a nice original paper on a model of Cosserat continuum. Remarkably enough Aero is still active at the moment of writing this book (2012) and he considers nonlinear effects in media that are also generalized continua.

E. Aero did not restrict himself by micropolar solids; he also developed the model of micropolar viscous fluids (Aero et al., 1965). Later the model was generalized by Eringen (1966b) by taking into account rotatory inertia. The micropolar hydrodynamics was applied to describe the behavior of magnetic liquids, polymer suspensions, liquid crystals, and other types of fluids with microstructure; see, for example, the books by Łukaszewicz (1999) and Eringen (2001). Throughout his life Aero considered the micropolar models of solids and fluids. Nowadays the Cosserat continuum has taken a significant place in Continuum mechanics among other generalized models of continua such as micromorphic continua, strain gradient media, and media with internal variables.

Eron Aero also contributed to the theory of liquid crystals developing new theory for nematics based on the use of couple stresses theory. However, similar results were obtained in parallel by the other scientists, and such models of liquid crystals are called Ericksen–Leslie or Eringen liquid crystals (de Gennes and Prost, 1993).

During the last years, huge experimental data has been collected in the area of the study of solid surfaces relief on the atomic level, crystal lattices changes, arising of singular defects, formation of new phases, and phase transformations under an influence of intensive outer forces, temperature, or electromagnetic fields. These phenomena are observed in experiments but cannot be described within the linear theory or weakly nonlinear theory of crystalline media. In the last years, E. Aero developed strongly nonlinear continuum theory of crystalline media whose complex lattice structure consists of two sub-lattices. He suggested a principle of translational symmetry that resulted in obtaining new nonlinear equations of motion. The solutions to these equations allow us to predict deep structural rearrangements of the lattice in the field of intensive power and thermal stresses: lowering of potential barriers, switching of the interatomic bonds, phase transitions, fragmentation of the lattice, etc.; thus, some modern experimental data may be explained.

The new governing highly nonlinear equations were obtained in the form of the sine-Gordon equation and its generalizations. The generalized equation is not integrable, and new methods were needed for finding their solutions. E. Aero and his coauthors developed a new procedure allowing them to obtain new solutions for multidimensional nonlinear equations in an explicit form. It concerns, in particular, the 3D sine-Gordon and the nonlinear Klein-Fock-Gordon equations.

In 2016 there appeared the Special Issue of the Mathematics and Mechanics of Solids (SAGE Publ.) on the occasion of his 80th anniversary; see Eremeyev et al. (2016) where Aero’s most important papers were listed.


  1. Aero EL, Kuvshinskii EV (1961) Fundamental equations of the theory of elastic media with rotationally interacting particles (english translation from the 1960 Russian edition). Sov Phys Solid State 2(7):1272–1281Google Scholar
  2. Aero EL, Bulygin AN, Kuvshinskii EV (1965) Asymmetric hydromechanics. J Appl Math Mech 29(2):333–346. Cited By (since 1996)36Google Scholar
  3. de Gennes PG, Prost J (1993) The physics of liquid crystals. Clarendon Press, OxfordGoogle Scholar
  4. Eremeyev VA, Porubov AV, Placidi L (2016) Special issue in honor of Eron L Aero. Math Mech Solids 21(1):3–5MathSciNetCrossRefzbMATHGoogle Scholar
  5. Eringen AC (1966a) Linear theory of micropolar elasticity. J Math Mech 15:909–923MathSciNetzbMATHGoogle Scholar
  6. Eringen AC (1966b) Theory of micropolar fluids. J Math Mech 16(1):1–18MathSciNetGoogle Scholar
  7. Eringen AC (1967) Theory of micropolar elasticity. Princeton University, PrincetonCrossRefzbMATHGoogle Scholar
  8. Eringen AC (2001) Microcontinuum field theory. II. Fluent media. Springer, New YorkzbMATHGoogle Scholar
  9. Kuvshinskii RV, Aero EL (1964) Continuum theory of asymmetric elasticity – the problem of internal rotation. Sov Phys Solid State 5(9):1892–1897MathSciNetGoogle Scholar
  10. Łukaszewicz G (1999) Micropolar fluids: theory and applications. Birkhäuser, BostonCrossRefzbMATHGoogle Scholar
  11. Maugin GA (2013) Continuum mechanics through the twentieth century. A concise historical perspective. Springer, DordrechtCrossRefzbMATHGoogle Scholar
  12. Maugin GA, Metrikine AV (eds) (2010) Mechanics of generalized continua: one hundred years after the cosserats. Springer, New YorkzbMATHGoogle Scholar
  13. Stojanović R (1969a) Mechanics of polar continua: theory and applications. CISM courses and lectures, vol 2. Springer, WienGoogle Scholar
  14. Stojanović R (1969b) Recent developments in the theory of polar continua. CISM courses and lectures, vol 27. Springer, WienGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Gdańsk University of TechnologyGdańskPoland
  2. 2.Institute for Problems in Mechanical EngineeringSt. PetersburgRussia
  3. 3.St. Petersburg State UniversitySt. PetersburgRussia
  4. 4.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia

Section editors and affiliations

  • Holm Altenbach
    • 1
  1. 1.Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für MaschinenbauOtto-von-Guericke-UniversitätMagdeburgGermany