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In the autosoliton view, the complete mathematical model of the seismic process taken as the deformation and fracture process of a loaded geomedium combines dynamic equations of solid mechanics and specific constitutive equations for geomedium rheology. These equations describe both the conventional stress-strain evolution due to the stress wave propagation with sound velocities, which are governed by special features of constitutive equations, and slow dynamics of the loaded strong medium. Numerical investigation is given to the generation of deformation autosolitons, front structure, and propagation of intra- and interfault deformation disturbances. Slow deformation disturbances in real geomedium elements are numerically modeled.

Doppler laser interferometry is used to measure the transient time between the slow quasi-stationary stage of damage accumulation in rock samples to the ultrafast catastrophic stage of failure as well as the duration of the autocatalytic stage of macroscopic fracture. Small rock samples are tested for compression and three-point bending, and the velocity of displacement of their lateral surfaces is measured up to macroscopic fracture. The surface velocity at the catastrophic stage proves to be three orders of magnitude higher than the average surface velocity at the quasi-stationary stage of damage accumulation. The transient time to catastrophic failure is estimated at 60–100 ms, and the duration of the ultrafast catastrophic failure stage is 15–20 ms for small marble samples. The transient stage is the process of self-organization of individual acts of fracture into the state of self-organized criticality. At this stage, the distribution of individual acts of fracture evolves into power-law distributions. A simple fracture model with power laws is proposed, which is in full agreement with the experimental data. The developed mathematical model is used to calculate fracture of small rock samples, reproducing uniaxial compression and three-point bending tests, as well as fracture in rock masses with mine openings. We also model the process of faulting and fracturing in the mountains of Central Altai, including the foreshock process, main event (the Chuya earthquake of September 27, 2003) and aftershock process. The calculated seismic process fully corresponds to the Gutenberg–Richter recurrence law, and the calculated aftershock process conforms to the Omori law.

In the paper, inelastic strain localization in homogeneous specimens and mesovolumes of a polycrystalline material is modeled based on the asymmetric theory of an elastoplastic Cosserat continuum in a two-dimensional formulation for plane strain. It is assumed that rotational deformation in loaded materials occurs due to the development of localized plastic deformation as well as bending and torsion of the material lattice at the micro- and nanoscale levels. For this reason, the parameters of the micropolar model are considered as functions of inelastic strain for each local mesovolume of the continuum. It is shown that the observed parabolic hardening can be attributed to a large extent to the development of rotational deformation modes, bending and torsion, and appearance of couple stresses in the loaded material. The modeling results indicate that if rotational deformation is stopped in the loaded material, its accommodation capacity decreases, the local and macroscopic inelastic strains sharply increase, leading to a much more rapid formation of fracture structures. Conversely, the formation of meso- and nanoscale substructures with high lattice curvature in materials promotes the activation of rotational deformation modes, reduction of localized strains, and relaxation of stress concentrators.

The operating characteristics of machine parts and units are defined in many respects by the physical and mechanical properties of their surface layers. Unfortunately, it is still not quite clear what parameters and mechanisms are responsible for one or another modification of surface layer properties. In this context, computer modeling techniques can be a useful tool in studying the variation of surface properties in contact interaction and run-in. Of fundamental importance is the possibility to consider the processes occurring on nanoscales and scales of individual atoms. In the work, loading conditions in plastic surface deformation was reproduced on the macroscale (traditional approach), atomic scale, and mesoscale by computer modeling with the finite element method, movable cellular automata method, and molecular dynamics method. The modeling results are in good qualitative agreement with data of experimental measurements.

The paper considers 3D movable cellular automata (MCA) models of contact interactions involved in nanoindentation, sclerometry, and tribospectroscopy. The system under study is a titanium substrate with a harden coating. The substrate and coating materials are both described in the elastoplastic approximation. It is shown that the MCA method of numerical simulation provides correct description of the contact interaction of elastoplastic materials under different types of loads with explicit account for fracture. The possibility to detect damages in ma surface layers from friction force estimates is assessed.

The paper studies the generation and evolution of dynamic vortex structures in a material on different structural scales. It is shown that the generation of dynamic vortex structures can be the main accommodation mechanism in a material under external mechanical loading. On the microscale, these structures can provide inter-granular sliding and grain boundary migration with anomalously high rates. On higher structural scales, their evolution can be the main process responsible for nucleation and propagation of cracks, fragmentation of material, formation of a “quasiliquid” layer in friction pairs, etc. The data and conclusions derived from the study are confirmed by numerical calculations for different types of materials in the framework of molecular dynamics and movable cellular automaton methods.

Dynamics simulation of burnishing of a thin steel layer beneath an indenter applied with a constant force and then moving with a constant velocity was performed by the finite element method in the plane strain approximation. The indenter was modeled by a perfectly rigid body, and the steel was modeled by an elastoplastic body with isotropic hardening according to an experimentally defined law. The regularities of changes in the stressstrain state of the material near the treated surface were studied and mechanisms of the formation of a nanostructured layer were disclosed. The effect of the friction coefficient and the burnishing force on the height of a bulge of edged material was analyzed. The results of studies agree well with experimental data. © 2013 Pleiades Publishing, Ltd.

The paper concerns the development of a formalism of the movable cellular automata method for simulation of consolidated heterogeneous elastoplastic media at different scale levels. Using the developed formalism as the basis, an approach was formulated for construction of structural models that describe mesoscopic response (including fracture) of heterogeneous media to loading with regard to hierarchical organization of their internal structure. In the approach, the effect of structural scale levels higher than the level under consideration is taken into account by a technique combining the particle method and conventional methods of continuum mechanics. The effect of lower structural scale levels is taken into account by determining integral response characteristics of lower-scale representative volumes and by specifying appropriate values of particle interaction parameters. The proposed formalism was advanced for description of contrast heterogeneous media whose components can assume different aggregate states. The potentialities of the particle method for description of hierarchically organized media are illustrated by studying the response and fracture mechanisms of materials, including contrast media, with a developed porous structure.

In the framework of the method of movable cellular automata, an approach is proposed to multilevel description of deformation and fracture of brittle porous media with a single maximum in the pore size distribution histogram. In the approach, the effective response function of a cellular automaton is defined through direct simulation of the representative volume of a porous medium. A hierarchical model is developed for the mechanical behavior of ZrO 2 -based ceramics with the pore size comparable with the average grain size under shear and uniaxial compression. The developed approach is analyzed for feasibility of taking into account the spatial distribution nonuni-formity of strength properties of porous media by varying the automata interaction parameters in stochastically chosen directions. It is shown that this method of considering the nonuniformity holds much promise for multilevel description of porous media with a hierarchical pore space structure.

The paper demonstrates the feasibility of spectral analysis of acoustic vibrations and friction resistance force for studying the behavior, structure and properties of surface layers and coatings. Numerical simulation was performed on the nanoscopic scale with the use of the movable cellular automaton method. A method of analysis of elastic waves based on time dependences of velocity components, pressure and stress intensity at a certain point of the counterbody surface was proposed. The main peaks due to eigenfrequencies of the system, geometric and adhesion parameters of the model and the roughness of the interacting surfaces were identified in the obtained spectra. It is shown that the pressure spectra in the model are qualitatively similar to acoustic spectra in actual experiment. The feasibility of tribospectroscopic analysis based on calculation of the friction force for diagnostics of nanoscopic heterogeneities and discontinuities in a surface layer of thickness up to 100 nm is given theoretical grounds. The results of studies demonstrate the possibility of estimating the parameters of nanoscopic discontinuities such as the characteristic spatial period and linear dimensions. The applications of the proposed method as a promising nondestructive technique for studies of the behavior and diagnostics of the structure and damages in coatings and surface layers of nanoscopic thickness are discussed.

The paper discusses the problem of rotation in the framework of the particle method. It is shown that taking into account the rotatioi either as an independent degree of freedom or as a rotation of the surrounding allows adequate description of classical continua by th movable cellular automation method. Description of more complex media, for example micropolar media, requires consideration of th rotation by both methods with an independent degree of freedom taken as an independent rotation.

A procedure for a multilevel computer simulation of friction and wear is proposed where numerical calculations at local contact scales by the method of movable cellular automata and a macroscopic phenomenological friction theory are chained together within a unified concept. For a mesoscopic simulation, use is made of the method of movable cellular automata in combination with numerical methods of continuum mechanics. Results obtained from a simulation of local contacts in contacting pairs of heterogeneous friction materials are reported. The effect of the initial surface microroughness on a quasi-fluid layer in the contact zone of plastic materials is examined. The macroscopic phenomenological model for friction describes spalling, reintegration of wear debris into the wear surfaces and mass transfer from one contacting body to the other, using stochastic differential equations. The parameters of the phenomenological equations are found solely by means of microscopic models for processes involved in a tribological contact. It is suggested that a simulation by the method of movable cellular automata be used to this end. The procedure developed enables the effective diffusion coefficient of the friction layer to be estimated. Identification of the parameters of the macroscopic model is made possible by simulating the processes operative at the nanoscale level thus bridging nano- and macroscale levels.

In the paper the method of discrete modeling (movable cellular automata method) and combined discrete-continuous description of the simulated medium are used to analyze processes occurring in the local contact of the automotive brake system. The characteristic size of the considered region is 1.5 μm. The following contact situation is simulated: steel fiber coated by an iron oxide film as the brake pad and pearlitic steel also coated by an iron oxide layer as the disc. On the assumption of oxide layer wearing we simulate the iron oxide - iron oxide, iron oxide - metal and metal - metal contacts. The calculation results for the friction coefficient for various contact situations give quite adequate values. For example, for the oxide - oxide system the calculated coefficient is approximately equal to 0.4, while for the metal - metal contact the obtained value varies from 0.7 to 0.9. Analysis of a set of the obtained results allows concluding that oxide is formed more rapidly than the sliding layer, which in turn makes the friction coefficient value stabilized.

The discrete movable cellular automaton method (MCA-method) is used to develop a technique for determining shear components of the stress and strain tensor in an arbitrary elementary volume of the specimen. We perform calculations for different calcium distributions through the coating thickness, which correspond to different methods of calcium distribution or different time of its being in the organism. The calculation results allow us to evaluate elastic properties as well as shear strains and stresses depending on the distribution of elements in the coating. For the chosen coating compositions we determine calcium distributions at which the shear stress and strain values in the coating are maximum and minimum.