Search

In the paper, we consider the tangential contact of single microasperities of the interacting surfaces the mechanical characteristics of which are close to the characteristics of typical rail steels. Using computer simulation by the method of discrete elements, we study the influence of the parameters of adhesive interaction of both external and internal surfaces on the regime of wear of asperities. It has been established that with increasing adhesion work, the wear regime changes from slipping (low wear) to grinding or brittle fracture of asperities (high wear), and this change is of threshold nature. An empirical sigmoid dependence of the location of the boundary between the two wear regimes (namely, the threshold value of the adhesive stress) on the value of the material hardening coefficient has been established. It is shown that the logistic nature of this dependence is due to the competition of two mechanisms of elastic strain energy dissipation, which determine the wear regime. These are plastic deformation and adhesion of the contacting surfaces. Special discussion is devoted to the influence of the scale factor on the threshold values of the mechanical characteristics of the material which provide the change of the wear regime.

Methods of particles are now recognized as an effective tool for numerical modeling of dynamic mechanical and coupled processes in solids and liquids. This chapter is devoted to a brief review of recent advances in the development of the popular particle-based discrete element method (DEM). DEM is conventionally considered as a highly specialized technique for modeling the flow of granular media and the fracture of brittle materials at micro- and mesoscopic scales. However, in the last decade, great progress has been made in the development of the formalism of this method. It is largely associated with the works of the scientific group of Professor S. G. Psakhie. The most important achievement of this group is a generalized formulation of the method of homogeneously deformable discrete elements. In the chapter, we describe keystones of this implementation of DEM and a universal approach that allows one to apply various rheological models of materials (including coupled models of porous fluid-saturated solids) to a discrete element. The new formalism makes possible qualitative expansion of the scope of application of the particle-based discrete element technique to materials with various rheological properties and to the range of considered scales form microscopic to macroscopic. The capabilities of this method are especially in demand in the study of the features of contact interaction of materials. To demonstrate these capabilities, we briefly review two recent applications concerning (a) the effect of adhesive interaction on the regime of wear of surface asperities under tangential contact of bodies and (b) the nonmonotonic dependence of the stress concentration in the neck of the human femur on the dynamics of hip joint contact loading.

The paper summarizes the results of long-term field research in the dynamics of the Baikal ice cover as a multiscale block medium similar to the lithosphere in structure, rheology, and seismotectonic features. The analysis covers data on deformation, seismicity, and contact interaction modes as well as on meteorological factors responsible for dynamic fracture of ice plates and strong ice shocks with earthquake-like vibrations. Similarity between seismic features in ice interface zones and zones of tectonic subduction, collision, and shear is discussed. Reasoning from dynamic analogies and similarities of destruction processes in the ice and lithosphere, the research data can help solving fundamental and applied problems, particularly those of earthquake prediction and assessment of contact interactions between lithospheric plates in fault zones.

The paper is devoted to the numerical study of the dependence of uniaxial compressive strength of permeable fluid-saturated brittle solids on the loading rate. We analyzed the influence of strain rate, sample size, permeability of the material, fluid viscosity and a coefficient of the influence of pore pressure on the stress state of solid skeleton. We have shown that dynamic values of elastic modulus and strength of the sample is a unique nonlinear sigmoid-like function of the dimensionless parameter that characterizes the ratio of applied strain rate to interstitial fluid flow rate. We proposed the unified approximating function, which describes numerically derived dependences with good accuracy. The results of the study are relevant for estimating and forecasting dynamic compressive strength of the samples of different fluid-saturated brittle solids. Moreover, the proposed expression can be applied to determine unknown values of the fluid effect constants on the basis of reducing the experimental data to a unified curve.

We numerically calculated the coefficient of friction between a rigid cone and a viscoelastic Kelvin body under step-wise change of the velocity of sliding. The time dependence of the coefficient of friction has been empirically approximated. We show that the transition process has different character for the cases of increasing and decreasing of the sliding velocity.

In the paper, we developed a macroscopic discrete element model of permeable fluid-saturated materials with solid skeleton characterized by viscoelastic rheological properties. The Biot’s linear model of poroelasticity was used as a mathematical basis for describing the mechanical interrelation between the solid skeleton and interstitial fluid. Using this model, we numerically studied the dependences of the effective Young’s modulus and strength of fluid-saturated viscoelastic materials on the loading rate, sample size and the mechanical parameters, which determine the relaxation time of the solid-phase skeleton and the time scale of redistribution of fluid in the pore space. We revealed two dimensionless control parameters that determine the dynamic values of the effective mechanical characteristics of the samples under compression loading. We obtained the general relations that describe the above-mentioned dependences in terms of the two proposed control parameters. These relations have a logistic nature and are described by sigmoid functions. The importance of the proposed empirical expressions is determined by the possibility of their application for predicting the mechanical response of fluid-saturated materials of different nature (bone tissue, rocks, porous materials with polymeric skeleton, including elastomers, etc.) under dynamic loading.

In the paper, we developed a discrete element model of adhesive interaction of materials with taking into account the “cold welding” effect. Based on this model, we carried out a detailed analysis of the factors controlling regimes of adhesive wear for elastic-plastic materials with non-ideal plasticity. We proposed an empirical criterion of transition from “breakaway” to “grinding” regime of wear. The extended form of the given criterion takes into account the dependence of material strength on hydrostatic pressure.

We study the problem of tangential frictional contact in the presence of adhesion. The model can be considered as a generalization of the theory by Cattaneo and Mindlin to the case where there are “long range adhesive interactions” between the contacting surfaces, which exert an additional pressure on the surfaces even in the absence of an external normal force. The adhesion forces are described by the Dugdale model and the tangential forces in the contact by Coulomb’s law of dry friction. These approximations allow obtaining an analytical solution for the tangential contact problem of a rigid parabolic indenter and a half-space. As in the case of nonadhesive contact, application of an arbitrarily small tangential force leads to slip in the narrow ring-shaped area near the contact boundary. Further increase in tangential load leads to a decrease in the radius of the stick region until sliding expands to the entire contact region. The obtained analytical solution shows that the main governing param...

The paper studies how the stress state of the interface between structural elements in a block-structured medium affects its deformation response to dynamic loading. It is shown that the normalized shear stress and mean stress are the major factors that determine the deformation response of the interface. We propose to describe the dependence of the value of induced irreversible displacement at the interface on the normalized shear stress using a logistic function. The central point of this function is the point of transition from the quasi-elastic to quasi-plastic stage of the interface shear deformation. The obtained empirical dependences are important for understanding the mechanism of irreversible strain accumulation in fault zone fragments and, particularly, for the development of an earlier proposed approach to estimate the characteristic level of active shear stresses in separate tectonic fault regions.

Adhesive contact with exponential adhesive interaction is simulated with the use of the method of dimensionality reduction. The developed procedure is illustrated with an example of adhesion of a cylindrical punch and an elastic half space. However, it is general and can be used for any form of interaction potential and any form of indenter.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 2167, 020075 (2019) and may be found at https://doi.org/10.1063/1.5131942. The paper reviews tangential adhesive contact of single asperities of elastic-plastic body surfaces. With the help of discrete element method we carried out a parametric study of influence of the parameters of adhesive interaction of the surfaces on the regime of asperity wear. It was established that with the adhesion work increase, the wear regime evolves from the mutual slippage of asperities to their attrition or brittle fracture, therewith the regime change has threshold nature. We obtained an empirical sigmoidal dependence of the threshold value of adhesion strength separating the slippage and attrition regimes on the strain-hardening coefficient of the material The results of the research make an important contribution to understanding the mechanisms that determine the development and intensity of wear in dry contact with adhesion.

A liquid in a pore volume influences on a strength of porous permeable media, both brittle and elastic-plastic. Despite of the dilation of the latter, a pore pressure of a liquid can remain nonzero under constrained shear loading. In the result, a liquid pressure contribute into a stress-strain state of a medium, and, correspondingly, into a strength. On the other hand, a liquid pressure depends on transportation properties of a medium namely on porosity and permeability, where the latter is determined by a characteristic diameter of filtration channels in a solid skeleton. A superposition and interplay of filtration of a liquid and its compression in pores originates a dynamical distribution of a pore pressure in a bulk of material. The non-linearity and interconnectedness of the mentioned processes clearly demonstrate the necessity of application of numerical methods for a studying of strength properties of such permeable liquid-filled media. We have studied a dependence of shear strength of a water-filled elastic-plastic sample under constrained conditions in the framework of the hybrid cellular automaton method that represents a variation of a DEM with explicit account of a liquid in pores. An elastic-plastic sample has been mounted between purely elastic permeable blocks that moved in lateral direction with a constant velocity. There were periodic boundary conditions in lateral direction. In order to create an initial hydrostatic compression in a volume, a pre-loading was performed before shearing. The elastic blocks and the sample had the same values of porosity, permeability, elastic moduli etc. We varied the values of the shear rate, the value of hydrostatic compression, width of the sample and the permeability. We have found that the strength of the sample depends on a cooperation of the following processes: 1) increase of a mean stress in a medium under shear; 2) dilation of elastic-plastic sample after reaching a yield point; 3) mass transfer of a fluid in a pore volume of a sample and elastic blocks and 4) redistribution of a fluid pressure due to its mass transfer. The observed effects together with the results of numerical simulations allowed us to suggest a binomial dependence of shear strength of an elastic-plastic sample on permeability, loading parameters and geometry of a sample. The first term of this dependence describes the exponential decrease of strength of a sample due to the decrease of effective stiffness of the elastic blocks under outflow of a liquid into an excess pore volume of a sample. Note that the latter leads to the decrease of the degree of constraint. The second term characterizes the influence of filtration on an increase of effective stiffness of the sample due to the growth of pore pressure of a liquid. This, in turn, leads to the increase of the degree of constraint of the sample. The parameters of the given dependence represent the combinations of the values of loading, width of a sample, its physical-mechanical properties, including permeability, and physical mechanical properties of a liquid.

This study shows the significant and nonlinear effect of the competition between dilation and fluid flow on the shear strength of constrained shear bands in fluid-saturated rocks. This effect is conditioned by the contribution of the pore pressure to the yield stress and strength. The pore pressure is controlled by the dilation of the pore space in the solid skeleton of the shear band during plastic deformation and by squeezing of pores in surrounding blocks by the dilating shear band due to the high stiffness of the host massif. A generalized equation has been derived to describe the dependence of the shear band strength on the ratio of strain rate to fluid flow rate.

We investigate the coefficient of friction between a rigid cone and an elastomer with account of local heating due to frictional dissipation. The elastomer is modeled as a simple Kelvin body and an exponential dependency of viscosity on temperature is assumed. We show that the coefficient of friction is a function of only two dimensionless variables depending on the normal force, sliding velocity, the parameter characterizing the temperature dependence as well as shear modulus, viscosity at the ambient temperature and the indenter slope. One of the mentioned dimensionless variables does not depend on velocity and determines uniquely the form of the dependence of the coefficient of friction on velocity. Depending on the value of this controlling variable, the cases of weak and strong influence of temperature effects can be distinguished. In the case of strong dependence, a generalization of the classical “master curve” procedure introduced by Grosch is suggested by using both horizontal and vertical shift factors.

We suggest a numerical procedure for rapid simulation of fretting wear in a contact of two bodies subjected to tangential oscillations with a small amplitude. The incremental wear in each point of contact area is calculated using the Reye–Archard–Khrushchov wear criterion. For applying this criterion, the distributions of pressure and relative displacements of bodies are required. These are calculated using the method of dimensionality reduction (MDR).

An approach to implementation of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of discrete element method (DEM) is proposed. The approach is based on constructing many-body forces of element–element interaction within the formalism of simply deformable element approximation of generalized concept of DEM. Implementation of the approach is shown by the example of the movable cellular automaton method, which integrates the possibilities of DEM and cellular automaton methods. For correct modeling of inelastic deformation and failure of heterogeneous materials the dilatational non-associated model of plastic flow is implemented within the formalism of DEM. The examples are presented which illustrate correctness of the developed mathematical formalism and its usefulness in analysis of various problems in mechanics of discontinua.

We study the problem of wear of a rotationally symmetric profile subjected to oscillations with small amplitude. Under these conditions, sliding occurs at the boundary of the contact area while the inner parts of the contact area may still stick. In a recent paper, Dimaki with colleagues proposed a numerically exact simulation procedure based on the method of dimensionality reduction (MDR). This drastically reduced the simulation time compared with conventional finite element simulations. The proposed simulation procedure requires carrying out the direct and the inverse MDR transformations in each time step. This is the main time consuming operation in the proposed method. However, solutions obtained with this method showed a remarkable simplicity of the development of wear profiles in the MDR space. In the present paper, we utilize these results to formulate an approximate model, in which the wear is simulated directly in the one-dimensional space without using integral transformations. This speeds up the simulations of wear by further several orders of magnitude.

Paper is devoted to development of structural and rheological model for investigation of peculiarities of deformation and fracture of metal-ceramic composites in the framework of movable cellular automaton method (one of the representatives of discrete element methods in computational mechanics). Developed model takes into account main features of internal structure of metal- ceramic composites, such as wide size distribution of reinforcing ceramic inclusions, presence of wide transition zones between inclusions and metallic binder, etc. Using this model influence of width of interphase boundaries on the strength, the value of the ultimate strain and fracture energy of metal-ceramic composites was theoretically investigated. It is shown that the formation in the material of relatively wide interphase boundaries, characterized by a smooth change of the mechanical properties during the transition from the surface of ceramic inclusions into the volume of the binder, can significantly improve the mechanical properties (strength and fracture energy) of the metal-ceramic composite. This effect is connected with a significant decrease in stress gradient on the wide interphase boundaries.

The paper is concerned with the contact between the elastic bodies subjected to a constant normal load and a varying tangential loading in two directions of the contact plane. For uni-axial in-plane loading, the Cattaneo-Mindlin superposition principle can be applied even if the normal load is not constant but varies as well. However, this is generally not the case if the contact is periodically loaded in two perpendicular in-plane directions. The applicability of the Cattaneo-Mindlin superposition principle guarantees the applicability of the method of dimensionality reduction (MDR) which in the case of a uni-axial in-plane loading has the same accuracy as the Cattaneo-Mindlin theory. In the present paper we investigate whether it is possible to generalize the procedure used in the MDR for bi-axial in-plane loading. By comparison of the MDR-results with a complete three-dimensional numeric solution, we arrive at the conclusion that the exact mapping is not possible. However, the inaccuracy of the MDR solution is on the same order of magnitude as the inaccuracy of the Cattaneo-Mindlin theory itself. This means that the MDR can be also used as a good approximation for bi-axial in-plane loading.

In the work, a hybrid cellular automata method was developed to study behavioral peculiarities of heterogeneous materials and contrast media. The method is a combination of two approaches: classical and movable cellular automata methods. The method was verified through comparing simulation data on sorption of carbon dioxide in lignite and corresponding experimental data provided by researchers from Velenje Lignite Mine (Slovenia). The obtained estimates of model parameters were used in numerical simulation of the gas phase on the strength and fracture of lignite samples. It is shown that the presence of the gaseous atmosphere even of pressure 0.1 MPa changes the effective strength of the lignite sample and the character of their fracture. The developed method can be used to study behavioral peculiarities of complex multicomponent media such as coal beds in mine zones.

The paper reports on basic ideas of the method of reduction of dimensionality and demonstrates its efficiency in simulation of friction of elastomers having arbitrary linear rheology and a rigid rough surface with fractal relief. The fixation time of elastomer on a rigid surface before the onset of tangential motion is studied as a parameter affecting the static friction coefficient. It is also studied how the friction coefficient in steady-state sliding is affected by harmonic oscillations of normal pressing force.

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.

An algorithm for calculating the force of friction between a fractal rough solid surface and a model elastomer with arbitrary linear rheological properties has been developed based on the method of dimensionality reduction with application of a hierarchically organized memory. Using this method, it is possible to calculate the friction force between an elastomer and a solid surface with experimentally determined topography, taking into account both the broad spectrum of wave vectors (ranging from nanometers to centimeters) for real surfaces and the wide range of relaxation times (from nanoseconds to seconds).

The paper studies the mechanisms of strain localization at the interfaces of structural elements in quasi-2D block-structured (plate) systems. The model plate system is the ice cover of the Lake Baikal. The emphasis in the paper is on analyzing the relationship between intraplate strains and interplate displacements. It is shown that the activation of convergent interplate displacements and the development of subduction zones in the ice cover are due to an increase in tensile intraplate stress, and this is consistent with the main mechanisms of tectonic processes in the lithosphere. Analysis of the stress distribution allows the conclusion that the deformation mechanisms in the block-structured ice cover fit the concept of plate tectonics. The obtained results make it possible to estimate the characteristic tectonic stress (2–10% of the plate strength) at which convergent interplate displacements are activated. It is found that in individual regions of the plate system, anomalously high internal stress (up to 20–30% of the plate strength) can be reached resulting in fragmentation of structural blocks and involvement of the thus formed interfaces in deformation. It is demonstrated that with the so high internal stress, the deformation at the interplate boundaries is far from typical, and this can be considered as a precursor of coming dynamic seismogenic events.

The applicability of a tribospectral analysis to the detection of nanoscale inhomogeneities and discontinuities at the nanocoating-substrate interface has been substantiated theoretically. The approach put forward in this work is based on the measurement of the counterbody sliding resistance force coupled with an analysis of its frequency spectrum. A theoretical study on the potentialities and limitations of nanotribospectroscopy has been performed with the use of a computer simulation by the method of movable cellular automata. The results of the investigation have shown, among other things, the possibility to estimate a number of parameters of nanoscale discontinuities (characteristic spacing, linear size, etc.). To obtain reliable information on the defect structure and spacing, nanotribospectroscopy must be supplemented by other diagnostic methods. The design of a prototype nanotribospectrometer with spatial resolution up to 8 nm is described. Applications of the examined approach as a promising nondestructive-testing technique for assessment of nanostructured coating and surface layer damage are discussed.

The spaced monitoring system developed for relative displacements in a block-faulted geomedium enables the central time-lapse survey of movement of lengthy and spaced discontinuities in a wide range of temperatures and weather environment. The communication between the monitoring system units is wireless.

The field investigations carried out recently have shown that an effective model medium for studying geotectonic processes can be the ice cover of Lake Baikal, which is a classical example of hierarchically organized block-structured media. Many significant deformation mechanisms of the block-structured ice cover can be compared to the mechanisms known in geodynamics, such as spreading, subduction, pull-apart and other ones. The present paper contains the results of studying dynamic processes of formation and evolution of one of the mentioned deformation-induced structures in the Baikal ice cover, namely, an underride zone that can be considered as a subduction zone analog. It is shown that these processes can be induced by dynamic relaxation events related either to the formation of new interfaces (fragmentation of blocks) or to the activation of the existing but earlier inactive cracks. A supposition is made that fragmentation accompanied by releasing a large amount of elastic energy can be one of possible mechanisms of forming compression impulse, which is considered to be necessary for initiation of subduction in the lithosphere. The processes of forming underride and subduction zones are compared and their qualitative similarity is revealed. After examining the structure of contact between ice plates in the underride zone the conclusion was made that formation of the deformation-induced structure under consideration allows reducing the compression resistance of the plate boundary by orders of magnitude. This suggests that structures of subduction type make for an effective mechanism of realization of high inelastic deformations in block-structured media without noticeable stress growth.

The paper is devoted to theoretical investigation of peculiarities of inelastic deformation of porous brittle materials in constrained conditions. The study was based on computer-aided simulation by movable cellular automaton method. Analysis of the simulation results allowed to estimate values of some rheological parameters of porous brittle materials and to determine the limits of applicability of Mises–Schleicher equation for description of the inelastic deformation of such materials under axial compression in constrained conditions.

This paper presents a theoretical study of shear strength of an elastic-plastic water-filled interface between elastic permeable blocks under compression. The medium is described within the discrete element method. The relationship between the stress-strain state of the solid skeleton and pore pressure of a liquid is described in the framework of the Biot’s model of poroelasticity. The simulation demonstrates that shear strength of an elastic-plastic interface depends non-linearly on the values of permeability and loading to a great extent. We have proposed an empirical relation that approximates the obtained results of the numerical simulation in assumption of the interplay of dilation of the material and mass transfer of the liquid.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1783, 020041 (2016) and may be found at https://doi.org/10.1063/1.4966334. We have studied the coefficient of friction between a rigid parabolic indenter and a visco-elastic Kelvin foundation under step-wise change of sliding velocity. We have obtained analytical estimations for normal and tangential forces in a contact and their limiting values during transition process that occurs after a jump of sliding velocity. The results of numerical simulation are in good agreement with analytical estimates.

Investigation of real geological media faces significant difficulties related to the scale of objects (e.g., the length of fractures ranges from tens to thousands of kilometers) and significant durations of geological processes (long-term observations are needed to obtain reliable information about peculiarities of the response of fractures to forcing). Strains are accumulated over tens and even hundreds of years [1‐3]. Therefore, physical modeling using simplified and smaller-scale block schemes is a promising field in the study of tectonic processes in the Earth’s crust. The rheological characteristics, structural pattern, and forcing dynamics in such schemes can be considered similar to those in the Earth’s crust [4‐5]. The present paper is dedicated to study of the implication of the fracture-block system of ice cover in Lake Baikal and dynamics of its loading as an object for modeling geotectonic and seismogeological processes in the lithosphere. Investigations and observations were carried out during expeditions of the Siberian Division of the Russian Academy of Sciences in 2005‐2006 with the participation of scientists from

The paper is devoted to a qualitative analysis of friction of elastomers from the point of view of scales contributing to the force of friction. We argue that – contrary to widespread opinion – friction between a randomly rough self-affine fractal surface and an elastomer is not a multiscale phenomenon, but is governed mostly by the interplay of only two scales – as a rule the largest and the smallest scales of roughness of the contacting bodies. The hypothesis of two-scale character of elastomer friction is illustrated by computer simulations in the framework of the paradigm of Greenwood, Tabor and Grosch using a simplified one-dimensional model.

An approach to simulating exothermic chemical reactions based on the concept of cellular automata is described. The validity of the approach is analyzed using the results of simulating the propagation of the reaction front during self-propagating high-temperature synthesis in the Ni-Al system. Good agreement is obtained between simulated and experimental dependences of the propagation velocity of the front and the maximum combustion temperature on the initial heating temperature of the powder mixture. It is concluded that a correct description of the effect of porosity on the course of the exothermic reaction requires explicit allowance for the reaction kinetics, in particular, the spreading of the liquid phase.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1683, 020040 (2015) and may be found at https://doi.org/10.1063/1.4932730. We propose a simple and efficient model of wear of axially symmetric bodies in contact with a visco-elastic foundation based on the method of dimensionality reduction. The results of simulation of wear of a parabolic indenter have been demonstrated. It has been shown that dissipation due to viscosity of a material leads to increase the size of the worn region of an indenter. The noted effect is conditioned with an increase of effective shear modulus of visco-elastic material under sufficiently high velocities of tangential loading. The model can be generalized to a wide range of materials with complex visco-elastic properties.

The paper is devoted to development of a model of the “third body” in the framework of movable cellular automaton method to take account of interfaces in heterogeneous interfacial materials. The main feature of the developed approach is the ability of direct account of the width and rheology of interphase/grain boundaries as well as their non-equilibrium state. Results of the verification of the developed model showed that it can be effectively used to study the response of such interfacial materials, for which is hampered to us use “classical” approaches of implicit and explicit accounting interfaces in the framework of discrete element methods.

In this paper, a numerical study of the influence of the stress state of interface of the block medium structural elements on the deformation response of interface to the dynamic impacts. It is shown that the basic characteristics of the stress state determining the deformation response of the interface are the values of shear stress and mean stress. It is found that the dependence of the irreversible displacement at the interface zone initiated by dynamic impact on the reduced shear stress is described by the logistic function. Herewith, the influence of the mean stress and dynamic impact energy on the value of displacement initiated by dynamic impact can be taken into account by dependence of the logistic function numerator on these parameters.

We study theoretically and numerically the kinetics of the coefficient of friction of an elastomer due to abrupt changes of sliding velocity. Numerical simulations reveal the same qualitative behavior which has been observed experimentally on different classes of materials: the coefficient of friction first jumps and then relaxes to a new stationary value. The elastomer is modeled as a simple Kelvin body and the surface as a self-affine fractal with a Hurst exponent in the range from 0 to 1. Parameters of the jump of the coefficient of friction and the relaxation time are determined as functions of material and loading parameters. Depending on velocity and the Hurst exponent, relaxation of friction with characteristic length or characteristic time is observed.

The paper is devoted to theoretical investigation of the influence of gas pore pressure on the characteristics of mechanical response of gas-filled permeable materials and media. Investigation was based on computer-aided simulation by hybrid cellular automaton method. Mechanical response of the model gas-filled samples of young brown coal under unconfined (in absence of constraint) and constrained conditions was investigated. The simulation results showed that increase of the pore pressure of the gas acting on the solid skeleton leads to decrease in materials strength. This is due to the fact that the gas pressure makes an additional contribution to integral pressure acting in volume of the loaded medium. Consequences of this are earlier beginning of plastic deformation and fracture of the material. It should be noted that in the constrained conditions decreasing of material strength with increasing gas pore pressure has more pronounced nonlinear character, in comparison with similar tests for unconfined samples. This is due to the fact that loading of constrained material is accompanied by its massive cracking and, consequently, by a grater decrease of the strength characteristics of the medium.

A method of numerical simulation of liquid-saturated porous media, that represents a combination of particle method and finite-difference method, namely, the hybrid cellular automaton method was proposed. It allows taking into account inelastic deformations, dilation and fracture of solid skeleton as well as the influence of pore pressure on the stress state of the skeleton and the redistribution of a liquid in filtration volume of porous medium. The method was applied to study the influence of viscous compressible liquid in pores of material on its strength and fracture. It has been shown that the strength of brittle liquid-saturated specimens depends on the material properties and the geometry of porosity, the physical-mechanical properties of the liquid etc. The latter shows the topicality of application of numerical methods to study and predict strength properties of fluid-saturated media under loading.

In this Letter, we study the friction between a one-dimensional elastomer and a one-dimensional rigid body having a randomly rough surface. The elastomer is modeled as a simple Kelvin body and the surface as self-affine fractal having a Hurst exponent $H$ in the range from 0 to 1. The resulting frictional force as a function of velocity always shows a typical structure: it first increases linearly, achieves a plateau and finally drops to another constant level. The coefficient of friction on the plateau depends only weakly on the normal force. At lower velocities, the coefficient of friction depends on two dimensionless combinations of normal force, sliding velocity, shear modulus, viscosity, rms roughness, rms surface gradient, the linear size of the system, and the Hurst exponent. We discuss the physical nature of different regions of the law of friction and suggest an analytical relation describing the coefficient of friction in a wide range of loading conditions. An important implication of the analytical result is the extension of the well-known ``master curve procedure'' to the dependencies on the normal force and the size of the system.