LABORATORY OF MECHANICS OF HETEROGENEOUS MEDIA
Research lines
Physical mesomechanics of materials.
- Development of mathematical models of heterogeneous media.
- Numerical study of deformation and fracture at the meso- and macrolevels under dynamic and quasistatic loading.
- Simulation of shock wave processes.
- Geomechanics and rock mechanics.
Basic research results
- An evolutionary approach was de
veloped to simulation of deformation processes in solids that are considered as hierarchically organized nonlinear dynamic systems. During the evolution of solids, their self-organization takes place giving rise to a hierarchy of blocks of different scales. The principle of fractal divisibility of solids was found according to which fracture begins with interatomic distances and continues up to the scale of tectonic plates. The scales in the hierarchy obey the golden ratio law or the Fibonacci law: each successive scale is the sum of two preceding scales, and the ratio of two consecutive scales is equal to Ф = 1.6180339... This principle is representative of the universal natural law of increment (decrement), in our case, in scales of destruction, and is responsible for self-similarity of fracture. The forming scale hierarchies of destruction (blocks) are multifractal structures. - Hierarchical models of heterogeneous materials were developed through combining various known and original models. The original models developed in the laboratory are (а) micropolar model of mesoscale plastic deformation of polycrystals in which the velocity of internal rotation is a function of accumulated plastic strain; (b) model of slow plastic flows based on the two-limit criterion of elastoplastic transition; (c) modified version of the Nikolaevsky model for describing damage accumulation in geomedia; (d) relaxation models of elastoplastic response based on dislocation kinetics and on the concept of viscous evolution of plastic deformation under dynamic action; (e) model of mesoscale fracture based on a modified version of the Hubert criterion, etc. The use of the developed models in numerical experiments made it possible to reveal peculiarities of the evolution of inelastic deformation and fracture at the meso- and macrolevels due to the structural influence of different materials.
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he use of the developed models and software tools in solving an important applied problem - fracture of coals - made it possible to reveal a relationship between the coal microstructure and the fractional content of coal dust particles in coal production under specified loading conditions. An algorithm was developed to determine the dust weight fractions through calculation data processing. A range of total porosity (3-7%) was found in which the mechanical behavior of a coal mesovolume changes qualitatively during liquid infusion into the pore space. - An approach was developed to 3D simulation of deformation and fracture of heterogeneous materials with explicit consideration for internal interfaces. A method was proposed for generating 3D model structures of various types, including polycrystalline alloys, composite materials with phases of different geometry, porous ceramics, materials with coatings, etc. The effect of internal interfaces and surfaces on deformation and fracture in 3D heterogeneous materials at the meso- and macrolevels was studied in numerical experiments.
- A mathematical model and appropriate computational algorithms were developed to study deformation and fracture of geomaterials; the developed model and algorithms are based on solving a system of dynamic equations of an elastoplastic medium with the use of several models that take into account internal friction, dilatancy and accumulation of damages under deformation. The results of numerical calculations demonstrate the formation of a periodic system of localized shear in a layer of geomedium, bands of localized compaction and localized shear with compaction, and also the possibility of development of inelastic deformation with alternate compaction and loosening in regions of increased porosity and fracturing.
- Dynamic models of deformation of solids with translational and rotational defects were developed in the framework of the gauge approach; the properties of the models and the mechanisms of deformation were investigated.