Vitaly Kuzkin

Peter the Great St.Petersburg Polytechnic University | SPBSTU · Department of Theoretical Mechanics

We investigate the unsteady heat (energy) transport in an infinite mass-in-mass chain with a given initial temperature profile. The chain consists of two sublattices: the β-Fermi-Pasta-Ulam-Tsingou (FPUT) chain and oscillators (of a different mass) connected to each FPUT particle. Initial conditions are such that initial kinetic temperatures of the...

We study the evolution of initial temperature profiles in a two-dimensional isolated harmonic graphene lattice. Two heat transfer problems are solved analytically and numerically. In the first problem, the evolution of a spatially sinusoidal initial temperature profile is considered. This profile is usually generated in real experiments based on th...

Previous analyses of the flow of low-Reynolds-number, viscous gravity currents down inclined planes are investigated further and extended. Particular emphasis is on the motion of the fluid front and tail, which previous analyses treated somewhat cavalierly. We obtain reliable, approximate, analytic solutions in these regions, the accuracies of whic...

We present a review of the results in the field of discrete thermomechanics that have been achieved in the Institute for Problems in Mechanical Engineering RAS over the past decade. The focus is set on the novel approach for analytical description of non-equilibrium thermomechanical processes in crystalline solids. One, two, and three-dimensional p...

The kinetic theory is widely used in the description of thermal transport at the micro- and nanoscale. In the theory, it is assumed that heat is carried by quasi-particles, obeying the Boltzmann transport equation. These quasi-particles are sometimes associated with phonons. However, since phonons are not localized in physical space, they cannot pl...

The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the $\beta$-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation. Two different types of initial conditions are used to show that either one gives the same result as the number o...

The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the β-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation. Two different types of initial conditions are used to show that either one gives the same result as the number of real...

We study thermal equilibration in face-centered cubic lattices with harmonic and anharmonic (Lennard-Jones) interactions. Initial conditions are chosen such that the kinetic temperatures, corresponding to three spatial directions, are different. We show that in the anharmonic case the approach to thermal equilibrium has two time scales. The first t...

The effect of discrete breathers (DBs) on macroscopic properties of the Fermi-Pasta-Ulam chain with symmetric and asymmetric potentials is investigated. The total to kinetic energy ratio (related to specific heat), stress (related to thermal expansion), and Young’s modulus are monitored during the development of modulational instability of the zone...

We study conversion of thermal energy to mechanical energy and vice versa in an α-Fermi-Pasta-Ulam-Tsingou (FPUT) chain with a spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This phenome...

We study dynamical phenomena in a harmonic graphene (honeycomb) lattice, consisting of equal particles connected by linear and angular springs. Equations of in-plane motion for the lattice are derived. Initial conditions typical for molecular dynamic modelling are considered. Particles have random initial velocities and zero displacements. In this...

We study thermal processes in infinite harmonic crystals having a unit cell with an arbitrary number of particles. Initially, particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main goal is to calculate spatial distribution of kinetic temperatures, corresponding to degrees of freedom of t...

We study conversion of thermal energy to mechanical energy and vice versa in $\alpha$-FPU chain with spatially sinusoidal profile of initial temperature. We show analytically that thermal expansion and temperature oscillations, caused by quasiballistic heat transport, excite mechanical vibrations with growing amplitude. This new phenomenon is refer...

We study deformation and fracture of a brittle material under mixed quasi-static loading. Numerical simulations of deformation of a cubic sample containing a single crack are carried out using the particle dynamics method. Effect of ratio of compressive and shear loads on energy of fracture initiation is investigated for two crack shapes and variou...

We study transient thermal processes in infinite harmonic crystals having a unit cell with an arbitrary number of particles. Initially, particles have zero displacements and random velocities such that spatial distribution of temperature is uniform. Initial kinetic and potential energies are different and therefore the system is far from thermal eq...

For a number of crystals the existence of spatially localized nonlinear vibrational modes, called discrete breathers (DBs) or intrinsic localized modes (ILMs), has been demonstrated using molecular dynamics and in a few cases the first-principle simulations. High-resolution imaging of DBs is a challenging task due to their relatively short lifetime...

We consider dynamics of a one-dimensional harmonic chain with harmonic on-site potential subjected to kinematic and force loadings. Under kinematic loading, a particle in the chain is displaced according to sinusoidal law. Under force loading, a harmonic force is applied to a particle. Dependence of the total energy supplied to the chain on loading...

A new scalable and efficient implementation of the mesoscopic distinct element method for massively parallel numerical simulations of carbon nanotube systems is introduced. Carbon nanotubes are represented as chains of rigid bodies, linked by elastic bonds and dispersive van der Waals (vdW) forces. The enhanced vector model formalism of the elastic...

We consider the effective elastic properties of cracked solids, and verify the hypothesis that the effect of crack interactions on the overall anisotropy-its type and orientation-is negligible (even though the effect on the overall elastic constants may be strong), provided crack centers are located randomly. This hypothesis is confirmed by computa...

Transition to thermal equilibrium in a two-dimensional harmonic triangular lattice with nearest neighbor interactions is investigated. Initial conditions, typical for molecular dynamics simulations, are considered. Initially, particles have uncorrelated random velocities, corresponding to initial kinetic temperature of the system, and zero displace...

Elastic properties of three-dimensional lattices are usually anisotropic. This fact limits the range of applicability of lattice models in solid mechanics problems. In the present paper, we propose a simple three-dimensional lattice model with isotropic elastic properties. A quasi-random lattice is generated by randomly displacing particles of the...

A model (further referred to as the enhanced vector-based model or EVM) for elastic bonds in solids, composed of bonded particles is presented. The model can be applied for a description of elastic deformation of rocks, ceramics, concrete, nanocomposites, aerogels and other materials with structural elements interacting via forces and torques. A ma...

An approach for analytical description of thermal processes in harmonic lattices is presented. We cover longitudinal and transverse vibrations of chains and out-ofplane vibrations of two-dimensional lattices with interactions of an arbitrary number of neighbors. Motion of each particle is governed by a single scalar equation and therefore the notio...

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated numerically for different amplitudes $A$ and frequencies $\omega$ within the linear phonon band. The results...

A simple approach for calculation of anisotropic effective elastic properties of cracked materials is presented. Square computational domain containing randomly distributed cracks under plane strain conditions is considered. Effective elastic properties are expressed in terms of average displacement discontinuities on cracks in three test problems:...

An approach for transition from discrete to continuum description of thermomechanical behavior of solids is discussed. The transition is carried out for several perfect anharmonic crystals with pair force interactions: one-dimensional crystal, quasi-one-dimensional crystal (a chain possessing longitudinal and transverse motions), two and three-dime...

Пособие посвящено описанию быстрых и медленных тепловых процессов в гармонических кристаллах. К быстрым относятся выравнивание кинетический и потенциальной энергий и перераспределение энергии по пространственным направлениям. К медленным - процесс распространения тепла. Изложен оригинальный подход, позволяющий описывать данные процессы аналитически...

In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal, quasi-one-dimensional crystal (a chain possessing longitudinal and transversal motions), two- and tree-dimensional crystal...

A harmonic triangular lattice with a vacancy under imposed volumetric strain is considered. Simple asymptotic formula for the displacement field is derived. The formula has reasonable accuracy at all lattice nodes. Strain concentration factor, defined as the ratio of the maximal deformation of the bonds adjacent to the vacancy to the deformations o...

We consider two transient thermal processes in uniformly heated harmonic crystals: (i) equalibra-tion of kinetic and potential energies and (ii) redistribution of the kinetic energy among the spatial directions. Equations describing these two processes in two-dimensional and three-dimensional crystals are derived. Analytical solutions of these equa...

An approach for analytical description of unsteady heat transfer in infinite harmonic lattices is presented. Evolution of initial spatial distribution of kinetic temperature is investigated. Lattice dynamics equations are written in a form valid for one-dimensional chains and out-of-plane vibrations of two-dimensional lattices. The description of h...

В работе рассматриваются два высокочастотных тепловых процесса, происходящие при переходе гармонических кристаллов в состояние термодинамического равновесия: выравнивание кинетической и потенциальной энергий и перераспределение энергии по пространственным направлениям. Получено уравнение с детерминированными начальными условиями, описывающее оба пр...

Рассматриваются два переходных тепловых процесса, происходящие в однородно нагретых гармонических кристаллах: 1) выравнивание кинетической и потенциальной энергий; 2) перераспределение кинетической энергии по пространственным направлениям. Выведены уравнения, описывающие оба процесса в двухмерном и трехмерном случаях. Получены аналитические решения...

We consider two high frequency thermal processes in uniformly heated harmonic crystals relaxing towards equilibrium: (i) equilibration of kinetic and potential energies and (ii) redistribution of energy among spatial directions. Equation describing these processes with deterministic initial conditions is derived. Solution of the equation shows that...

Dynamic buckling of an elastic column under compression at constant speed is investigated assuming the first buckling mode. Two cases are considered: (i) an imperfect naturally curved column~(Hoff's statement), and (ii) a perfect column with an initial lateral deflection. The range of parameters where the maximum load supported by a column exceeds...

Linear elastic deformation of the two-dimensional triangular lattice with multiple vacancies is considered. Closed-form analytical expressions for displacement field in the lattice with doubly periodic system of vacancies are derived. Effective elastic moduli are calculated. The results are compared with the ones obtained by molecular dynamics simu...

The well-known issue with the absence of conservation of angular momentum in classical particle systems with periodic boundary conditions is addressed. It is shown that conventional theory based on Noether’s theorem fails to explain the simplest possible example, notably jumps of angular momentum in the case of single particle moving in a periodic...

The article presents results of numerical experiments performed to evaluate the effective rheological properties of a mixture of a fluid with solid particles. The numerical simulation of the Couette and Poiseuille flows shows that in the both cases, the effective viscosity and non-Newtonian properties of the suspension coincide to the accuracy of s...

Dynamic buckling behavior of a column (rod, beam) under constant rate compression is considered. The buckling is caused by prescribed motion of column ends toward each other with constant velocity. Simple model with one degree of freedom simulating static and dynamic buckling of a column is derived. In the case of small initial disturbances the mod...

Thermal expansion of a classical chain with pair interactions performing longitudinal and transverse vibrations is investigated. Corresponding equations of state are derived analytically using series expansions of pressure and thermal energy with respect to deformations of the bonds caused by thermal motion. In the first approximation the equation...

In this paper, we derive expressions for equivalent Cauchy and Piola stress tensors that can be applied to discrete solids and are exact for the case of homogeneous deformation. The main principles used for this derivation are material frame formulation, long wave approximation and decomposition of particle motion into continuum and thermal parts....

Jump detection and measurement is of particular interest in a wide range of sports, including snowboarding, skiing, skateboarding, wakeboarding, motorcycling, biking, gymnastics, and the high jump, among others. However, determining jump duration and height is often difficult and requires expert knowledge or visual analysis either in real-time or u...

The construction of pair interatomic potentials giving rise to negative thermal expansion (NTE) in single-component systems is discussed. In a paper by Rechtsman et. al. [J. Phys. Chem. A 2007] it is stated that the sufficient condition for NTE is positive third derivative of interatomic potential at equilibrium. In the present comment it is shown...

The paper presents results of numerical experiments performed to evaluate the effective viscosity of a fluid-proppant mixture, used in hydraulic fracturing. The results, obtained by two complimenting methods (the particle dynamics and the smoothed particle hydrodynamics), coincide to the accuracy of standard deviation. They provide an analytical eq...

A model (further referred to as the V model) for the simulation of granular solids, such as rocks, ceramics, concrete, nanocomposites, and agglomerates, composed of bonded particles (rigid bodies), is proposed. It is assumed that the bonds, usually representing some additional gluelike material connecting particles, cause both forces and torques ac...

The relations that describe the interactions of particles with rotational degrees of freedom in the study of mechanical properties of graphene are presented. Molecular-dynamic simulation of deformation and fracture of graphene upon tension is performed. During simulation, elastic, and strength characteristics of graphene are calculated. The propert...

We consider an approach to the derivation of thermodynamic equations of state by averaging the dynamic equations of particles of the crystal lattice. Microscopic analogs of macroscopic variables such as pressure, volume, and thermal energy are introduced. An analysis of the introduced variables together with the equations of motion permits obtainin...

In the present paper simple analytical expressions connecting bulk moduli for fullerenes C20 and C60 with stiffness of interatomic bond and geometrical characteristics of the fullerenes are derived. Ambiguities related to definition of the bulk modulus are discussed. Nonlinear volumetrical deformation of the fullerenes is considered. Pressure-volum...

The system of particles (atoms) interacting via multibody interatomic potential of general form is considered. Possible variants of partition for the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles...

Derivation of equivalent thermo-mechanical parameters for perfect crys- tals in the case of arbitrary interatomic potential is conducted. The approach based on the averaging of equations of motion is considered. Long wave ap- proximation is used to make link between the discrete system and equivalent continuum. Macroscopic thermo-mechanical paramet...

In the present paper the simplest 2D model of the material on the basis of fibrils is proposed. The single fibril is represented as two-layer stripe consisting of particles which interact via Lennard-Jones potential. In order to create the material fibrils are randomly added on the plane and connected in the places of the intersections. Molecular d...