Basic Scientific Results
Grigory Isaakovich Barenblatt
- Fracture mechanics. Fundamental mathematical model of elastic
body with cracks based on explicit introduction of cohesion forces, and
solutions of basic problems. Introduction of one of the basic characteristics
of fracture toughness: cohesion modulus. Basic model of the kinetics of crack
propagation. Applications to fracture problems of metals, rocks and polymers.
Similarity laws for brittle and quasi-brittle fracture. Scaling laws for fatigue cracks and multiple fracturing, model of small
fatigue cracks. Mathematical model of non-local damage accumulation.
model of self-oscillation, self-similar phenomena in fatigue fracture.
- Theory of fluid and gas flows in porous media.
Fundamental model of flow in fissurized porous rocks and solution of basic
problems. Asymptotic solutions of basic problems of unsteady
groundwater and gas
flows in porous media. Fundamental model of fluid flow in elasto-plastic porous
media and solution of basic problems. Non-equilibrium two-phase flow
in porous media
(capillary imbibition, water-oil displacement, solid phase
mathematical model, fundamental solutions. Mathematical model of
flow in fissurized-porous media. Mathematical model of very intense pulse in
groundwater flows in porous and fissurized porous rocks.
- Mechanics of non-classical deformable solids.
Mathematical models of neck propagation in polymers (deep analog of flame
propagation) and of thermal vibro-creep in polymers. Mathematical model of an impact of viscoplastic
body on a rigid obstacle.
- Turbulence. Turbulence in stratified fluids. Mathematical models of
the transport of heavy particles in turbulent flows. Basic model of turbulent
patch dynamics in stably stratified fluids, self-similar asymptotic laws;
relation to the oceanic microstructure. Mathematical model of non-steady heat
and mass transfer in stably stratified turbulent flows. Model of turbulent drag
reduction by polymeric additives. Mathematical models of turbulent burst and
turbulent shearless wake evolution. Mathematical model of laminar-turbulent
transition taking into account the evolution of pre-existing turbulence.
Mathematical model of temperature steps formation in stably
flows. Scaling laws for developed turbulent shear flows, in
particular for pipe,
boundary-layer flows and wall-jets. Mathematical models of dust storms and
- Self-similarities. Nonlinear waves and intermediate asymptotics.
Long-time work performed in general in close collaboration with
Ya. B. Zeldovich. Concepts of intermediate asymptotics, self-similar
asymptotics of the first and second kinds. Nonlinear eigenvalue problems.
Relation between intermediate asymptotics and renormalization groups.
Basic model of stability of self-similar solutions and travelling waves.
Contributions to the theory of combustion and thermal explosion. New model of
surface-tension-driven thin films.
These studies have led to new non-classical problems in mathematical
have had wide practical applications. The results have been published in many
papers and monographs and have wide resonance in world literature.