Andrey V. Dimaki

Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties

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).

Fast High-Resolution Simulation of the Gross Slip Wear of Axially Symmetric Contacts

ABSTRACT In the present article, we study the development of a wear profile in an axially symmetric contact under conditions of gross slip and assumption of the Reye-Archard wear criterion. Simulations are carried out using the method of dimensionality reduction and a full finite element method (FEM) formulation. The calculation time of the proposed model is several orders lower than that of FEM-based models and allows for much higher spatial resolution.

Effect of dynamic stress state perturbation on irreversible strain accumulation at interfaces in block-structured media

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.

On the role of scales in contact mechanics and friction between elastomers and randomly rough self-affine surfaces.

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.

Kinetics of the coefficient of friction of elastomers

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.

Ice Cover of Lake Baikal as a Model for Studying Tectonic Processes in the Earth's Crust

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 method of reduction of dimensionality and its application to simulation of elastomer friction under complex dynamic loads

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.

Coefficient of friction between a rigid conical indenter and a model elastomer: Influence of local frictional heating

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.

Influence of the state of interfaces on the character of local displacements in fault-block and interfacial media

We have studied the possibility of producing a directed action upon the process of local stress relaxation in interfacial media occurring in a complex stressed state by changing the state of boundaries between structural elements. The experiments were performed on the ice sheet of Lake Baikal, which represents a hierarchically organized fault-block structure and belongs to the class of interfacial media. It is shown that, by changing the state of boundaries between structural elements, it is possible to influence the regime of deformation of the interfacial medium as a whole. The general features of the observed effect are confirmed within the framework of a theoretical model.

Friction in an adhesive tangential contact in the Coulomb-Dugdale approximation

ABSTRACT 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 parameter of the problem is the parameter introduced by Maugis for the normal adhesive contact problem.