Laboratory for Discrete Models in Mechanics

The main goal
Simulation of the micro and macroscopic properties of materials using Molecular Dynamics and Particle Dynamics methods.

Head of laboratory
Prof. Anton M. Krivtsov.
Institute for Problems in Mechanical Engineering RAS, St. Petersburg, Russia.
Phone: +7-812-3277144,

Aristovich K.Y., M.Sc. student, SPbSPU, St. Petersburg, Russia.
Berinskiy I.E., M.Sc. student, SPbSPU, St. Petersburg, Russia.
Gilabert F.A., Ph.D. student, University of Seville, Spain.
Gonin O.G., Former member, St. Petersburg, Russia.
Efimov A.A., Ph.D. student, IPM RAS, St. Petersburg, Russia.
Le-Zaharov A.S., Ph.D. student, IPM RAS, St. Petersburg, Russia.
Loboda O.S., Ph.D. student, SPbSPU, St. Petersburg, Russia.
Kuzkin V.A., B.Sc. Student, SPbSPU, St. Petersburg, Russia.
Tkachev P.V., Ph.D. student, IPM RAS, St. Petersburg, Russia.
Tsaplin V.A., Research fellow, IPM RAS, St. Petersburg, Russia.
Vasilyev S.V., Research fellow, SPbSPU, St. Petersburg, Russia.
Volkovets I.B., M.Sc. student, SPbSPU, St. Petersburg, Russia.


  • Modeling of the mechanical and thermomechanical properties of nanostructured materials
  • Development of the effective methods for simulating plasticity and fracture
  • Description of the macroscopic properties of materials on the base of their microscopic structure

Current research

  • Analysis of mechanical properties for nanocrystalline materials
  • Computer design of nanomaterilals on the basis of molecular dynamics approach
  • Molecular dynamics analysis of mechanical and thermodynamic properties of mediums with microstructure
  • Computer analysis of the shock wave propagation in polycrystalline materials
  • Microstructure simulation of plasticity and fracture
  • Modeling dislocations in crystalline materials
  • Microstructure simulation of impact interaction of rigid bodies



The idea of the Particle Dynamics method is based on the concept that a material can be modeled by a large number of interacting particles, described by the classical laws of dynamics. Interaction between particles is determined by the interparticle potentials. The main feature of the interparticle potentials is repulsion at short range and attraction at long range. The initial conditions including two following components should be set before the simulation starts: space distribution of the particles (initial structure of the material) and distribution of the particles velocities (mechanical and thermal motion of the system in the initial state). Afterwards the simulation can be performed as a numeric solution of the Cauchy problem for the system of ordinary differential equations.

One of the best-developed variants of this method is the Molecular Dynamics. The last decades the Molecular Dynamics method has been intensively applied for investigation of the physical and chemical properties of materials. In the classical Molecular Dynamics the particles represent atoms and molecules. Nowadays the interatomic potentials for the most important materials are well known, that allows modeling molecular systems with a high rate of accuracy. The interest to modeling materials at the nanoscale level was drastically increased after discovering that materials with the nanoscale structure elements can possess essentially new mechanical and physical properties. Considering the current development of the computer techniques the Molecular Dynamics method allows simulating nearly any nanostructures with the highest level of accuracy. That is why this method has become the main computational method for the nanotechnologies.

For modeling materials at the macroscopic scale level, of course, it is impossible to leave the molecular concept as such. In this case particles should represent elements of the higher scale level (mesolevel), for example the level of material grains. Last years this approach appears to be an important alternative for the continuum mechanics in modeling plasticity and fracture. Following the tradition, this method frequently is called Molecular Dynamics, but more accurate name is Mesoparticle Dynamics or simply Particle dynamics. The important advantage of this method is that it needs far less a priori assumptions for the material properties. Indeed, even a simple Lennard-Jones potential allows simulating such complicated properties as plasticity, crack appearance, fracture, phase transitions, and thermomechanic behavior of materials. Each of these phenomena needs separate theory in the framework of the continuum mechanics. On contrary, Particle Dynamics method allows to obtain these effects almost automatically, while integrating equations of motion for each particle. In particular, irreversibility for the mechanical processes is achieving by transition of the long-wave mechanical energy to the thermal energy of the chaotic motion of the particles.

Interaction potential plays in the Particle Dynamics the same role as the constitutive equations in the continuum mechanics. But the structure of the interaction potential is far simpler, since the potential is a scalar function of a single variable the interparticle distance, while the constitutive equations are operators from tensor characteristics of the strain, and also they depend on the thermodynamic quantities. The particular shape of the interaction potential can be obtained from the comparison between macroscopic properties of the computer material and the real material. For the simplest (elastic, thermoelastic and some plastic) properties this comparison can be done analytically. In other cases the correspondence can be obtained from the computer experiments.


The group has developed original methodic for Particle Dynamics simulation. Modeling includes

  1. Preparing the initial configuration: setting the macroscopic shape, inner structure, macroscopic velocities, and microscopic (thermal) velocity fields.
  2. Simulation of the system dynamics (solving equations of motion) and recording the control and statistical parameters.
  3. Analysis of the data obtained during the computer experiment.

The program package for solving these tasks is developed. The main advantages of the software are convenience for setting the initial parameters, high efficiency of the numeric algorithms, and visualization of the modeling using advanced 3D computer graphics.

The main distinctions for the Particle Dynamics methods being developed by our group are

  1. Use of polycrystal particle arrangements.
  2. Account of the moment interaction and rotation energy for the particles.
  3. Optimized algorithms allowing simulating systems containing up to millions particles on simple personal computers.

For the large-scale computations the group is using the resources of the Joint Supercomputer Center.

Sample Publications

Here you can see list of sample publications and download them in PDF format.

You can contact us by

Phone: +7-812-3277144
Fax: +7-812-3214771
Mail: Institute for Problems in Mechanical Engineering RAS,
Bolshoy pr. V. O., 61, St. Petersburg, 199178, Russia