1. Introduced nanofracture mechanics
as the general, unified theory of dislocation emission, crack growth and
cleavage decohesion in terms of fundamental physical constants in nanoscale.
The approach was published in J. Applied Physics,
Soviet Applied Mechanics and Applied Mechanics
Reviews from 1986 to 1995, and supported by NSF grant. (Original
name for this approach was "quantum fracture mechanics", the
name "nanofracture mechanics" was suggested by Gilman). A parallel
work of Rice and Thomson in this area includes only nucleation of one
dislocation and cleavage decohesion.
2. Solved some
particular cases of long-standing Riemann and Riemann-Hilbert problems
for several functions (both linear and nonlinear) during 1961-65
under the influence of Gakhov's work in the area.
3. During 1961-1968, solved several
difficult mathematical problems of nonlinear mechanics with unknown boundaries
(in plasticity, elasticity, local buckling and hydrodynamics) using complex
variables. To the end, developed more capable methods as compared to those
advanced earlier by Kolosov, Muskhelishvili, Sherman, Sokolovsky, Galin,
Keldysh and Sedov in the area.
4. Generalized Griffith's
concept of fracture for arbitrary solids and continua (in 1967)
later co-offered by Landis and Begley for crack initiation (in 1972).
In the 80s, this concept was applied and developed by Atluri, Nishioka
and many other investigators in numerical and physical experiments as
applied to static and dynamic cracks in plastic materials.
5. Discovered the
invariant or path-independent integral (1967) which gives the strength
and driving force of crack tip singularities (in arbitrary elastic and
inelastic materials for both dynamic and static problems). The analogous
integral had been introduced earlier for point defect studies in static
elasticity by Eshelby and was later co-discovered by Rice (also, only
for static elasticity). This integral has found wide application in fracture
mechanics, at levels from atomic decohesion, to cracking in highly ductile
engineering structures, to landslides in clay slopes, and to large-scale
earthquake ruptures (in papers with Bykovtsev of 70s and 80s). It also
motivated a productive search for new conservation relations and invariant
integrals in other physical fields (in papers of 1978, 1979, 1983, 1987,1989).
6. Pioneered the so-called HRR
approach in fracture mechanics of power-law hardening
materials (1967) later co-discovered by Hutchinson, Rice and Rosengren.
7. Discovered super-penetration
effect of thin wing-shaped penetrators in solids at the Rayleigh speed.
Publications in J. Applied Mechanics,
Engineering Fracture Mechanics, Mechanics
of Materials, and other journals (1994-95) supported by NASA grant.
8. Discovered the interaction
law of relativistic charges (a generalized Coulomb's law) and
introduced the model for unusual fracturing effect of high-power relativistic
electron beams (with Borzykh, in J. Applied Physics,
9. Developed mathematical
description of stress accumulation and transfer around faults in the Earth's
crust (Physics of Earth, 1985;
and the book of 1987).
10. Discovered, with Galin, self-maintained
failure waves (1967) later re-discovered by Bless, and many others
in USA (1988-1995). The concept of structural bond energy release introduced
in this work stimulated the development of new energetic materials that
have found many military and civil applications.
11. Introduced 2D
theory of thermal stresses in thin films and bonding layers as applied
to high-speed microelectronics (J. Applied
Physics, 1994-95). The research is supported by AFOSR grant.
12. Solved the long-standing
problem of an isolated rigid fiber in an elastic space (1983)
attacked earlier by Larmor, Van Dyke, Landau, Lifshitz and Eshelby. The
method developed for solving this problem was applied to problems of pull-out,
push-in, and many other related problems of slender bodies (in publications
of 1983, 1985, 1987,1988,1995)
13. Developed an approach
to the localization of plastic deformation into shear bands using the
selection principle based on the concept of maximum energy dissipation
rate (1975). The concept was later applied by Slepyan to dynamic
14. Introduced the theory
of fluidization of particulate media (with Gupalo and Galin) that
found an application to design of chemical reactors (1969-1978).
15. Introduced the theory
of explosion effect in brittle materials as the counterpart to
the theory of Taylor and Grigorian for plastic materials.
16. Developed methods
of the functionally-invariant Smirnov-Sobolev's solutions in dynamic elasticity
and acoustics (with Afanasiev).
17. Proved that failure
criteria for brittle materials are generally path-dependent and do not
meet Drucker's postulate (with Germanovich, 1987-1995). The mathematical
theory of catastrophe was used to achieve the result.
18. Contributed to optimal
design by generalizing the concept of equistrength, introduced by Galileo
Galilei, for arbitrary structures. Predicted many equistrong configurations,
e.g. equistrong turbine blades, equistrong rotating disks, equistrong
holes, equistrong underground tunnel shapes, etc., using this concept
(1962-1995). The work was continued by Wheeler (as applied to minimum
stress concentration), Banichuk, Vigdergauz, Alimzhanov and other investigators
(supported by ARO grant).
19. Introduced the theory
of gas grifons around boreholes and erosion of fluid-infiltrated solids
under dams (1987).
20. Contributed to penetration
mechanics (1985, 1987, 1994).
21. Introduced the theory
of hydrogen embrittlement and corrosion fracture (1972-1981).
22. Introduced the theory
of fatigue crack growth (1968-1978)
23. Contributed to
contact and mixed problems of the theory of elasticity (1963-95).
24. Discovered an ample
class of boundary problems of the theory of elasticity, in which the
Saint-Venant's principle is not satisfied (1970).
25. Developed the Eshelby
's theory of point defects in solids (1984-1995).
26. Introduced the theory
of rock cutting (1987).
27. Developed classical fracture
Derived, with Barenblatt, energy release rate
in terms of stress intensity factors for arbitrary mixed-mode cracks
(co-derived, by Irvin, Kies and some other investigators).
Discovered, with Barenblatt, that the limiting
speed of crack propagation in a homogeneous material is the Rayleigh speed
(co-discovered by Broberg, Stroh, Wells and others).
Developed useful solutions for bimaterial interface
cracks later re-discovered by England, Rice, Sih, Hutchinson, Suo,
Salganik and other investigators.
Pioneered, with Barenblatt, the theory of cracks
in anisotropic materials. (This work was co-pioneered by Stroh).
Developed fractal fracture mechanics,
with Balankin and Ivanova (1996).
Developed creep crack growth theory in metals
Introduced the theory of delamination of laminate
structures and shells (1983).
Developed the theory of crack nucleation in metals
(in particular, according to Cottrell’s mechanism).
Developed fracture mechanics of composite materials
m. Developed fracture mechanics of rocks
Derived equation of energy release rate in terms
of stress intensity factor for a fast
propagating crack (1968). This equation was simultaneously co-discovered
by Eshelby, Atkinson, Kostrov, Freund and others.