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 quasibrittle fracture. Scaling laws for fatigue cracks and multiple fracturing, model of small
fatigue cracks. Mathematical model of nonlocal damage accumulation.
Mathematical
model of selfoscillation, selfsimilar 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 elastoplastic porous
media and solution of basic problems. Nonequilibrium twophase flow
in porous media
(capillary imbibition, wateroil displacement, solid phase
precipitation): basic
mathematical model, fundamental solutions. Mathematical model of
gascondensate
flow in fissurizedporous media. Mathematical model of very intense pulse in
groundwater flows in porous and fissurized porous rocks.
 Mechanics of nonclassical deformable solids.
Mathematical models of neck propagation in polymers (deep analog of flame
propagation) and of thermal vibrocreep 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, selfsimilar asymptotic laws;
relation to the oceanic microstructure. Mathematical model of nonsteady 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 laminarturbulent
transition taking into account the evolution of preexisting turbulence.
Mathematical model of temperature steps formation in stably
stratified turbulent
flows. Scaling laws for developed turbulent shear flows, in
particular for pipe,
boundarylayer flows and walljets. Mathematical models of dust storms and
tropical hurricanes.
 Selfsimilarities. Nonlinear waves and intermediate asymptotics.
Longtime work performed in general in close collaboration with
Ya. B. Zeldovich. Concepts of intermediate asymptotics, selfsimilar
asymptotics of the first and second kinds. Nonlinear eigenvalue problems.
Relation between intermediate asymptotics and renormalization groups.
Basic model of stability of selfsimilar solutions and travelling waves.
Contributions to the theory of combustion and thermal explosion. New model of
surfacetensiondriven thin films.
These studies have led to new nonclassical problems in mathematical
physics and
have had wide practical applications. The results have been published in many
papers and monographs and have wide resonance in world literature.
