A.B. Kiselev

Irregular traffic flow on a ring road

Abstract A model of irregular single-lane traffic flows on a ring road is proposed, with a number of fundamental differences from those traditionally examined in continuum mechanics. Even in the simplified version of the examination of single-lane traffic, the model enables a correct qualitative and quantitative description to be obtained of the conditions for ensuring maximum carrying capacity and for the occurrence and evolution of traffic jams on roads.

Mathematical modelling of dynamical deforming and combined microfracture of damageable thermoelastoviscoplastic medium

Publisher Summary Thermomechanical processes consist of mechanical, thermal, and structural ones which correlate between themselves. Structural processes in materials include formation and motion of the orders in crystal of metals, phase transition, split bonds between molecules in polymers, accumulation of microstructural damage etc. These processes are shown themselves on micro-level as irreversible deformations, thermal isolation, and fracture. Dynamic fracture is a complicated multistage process, including an appearance, development and confluence of micro defects and a formation of embryonic micro-cracks; they grow up to the break-up of the bodies with division into separate parts. Three basic types of dynamic fracture can be singled out: ductile, brittle, and the mechanism of adiabatic shear failure.

Elastoplastic models to describe experimental data on the spallation fracture under impact of plates

The processes of irreversible dynamic deformation and spallation fracture under plane impact of plates are numerically studied. The following two models for the behavior of the materials of the plates are used: a model of a damageable elastoplastic medium and a dislocation model. The computations were performed with the use of the TIS-1D software complex based on the method of separation into physical processes, the finite volume method, and moving Eulerian grids.

Elastoplastic problems in the uniaxially strained state approximation. Analytical and numerical solutions

A detailed study of shock and unloading waves is given in the uniaxially strained state approximation for elastoplastic problems. A numerical algorithm is briefly described. The TIS-1D software complex is verified in the case of one-dimensional problems. This software complex is based on the method of separation into physical processes and on the finite volume method using moving Eulerian grids.

Numerical modeling of irreversible dynamic deformation and fracture of an axisymmetric two-layer container filled with liquid on impact with a rigid obstacle

The results of numerical solution of the two-dimensional problem on the collision of an axisymmetric structure (a two-layer container filled with a liquid) and an absolutely rigid obstacle at various impact velocities are analyzed.

Unsteady expansion of thick-wall spherical and cylindrical viscoplastic shells

One-dimensional nonstationary problems of adiabatic expansion for thick-wall spherical and cylindrical viscoplastic shells are solved exactly under the assumption that, at the initial instant of time, the distributions of radial velocities satisfy the condition of incompressibility of the shell material. The resulting solutions can easily be modified for the case of compression of such shells.

A study on the fragmentation of space debris particles at high-speed collision

A mathematical model was previously proposed by the first author to evaluate the number of fragments and their mass distribution at high-speed collision of two space debris particles and to determine their velocities after collision. The constants used in this model are assumed to be temperature-independent. In this paper it is shown that the consideration of temperature effects due to high-speed collision of particles leads to the formation of smaller fragments and to a significant increase of their total number.

Computational Simulation of Irreversible Deforming and Fracture of Damageable Solids and Structures

Thermomechanical processes, which proceed in deformable solids under intensive dynamic loading, consist of mechanical, thermal and structural ones, which correlate themselves. The structural processes involve the formation, motion and interaction of defects in metallic crystals, phase transitions, the breaking of bonds between molecules in polymers, the accumulation of microstructural damages (pores, cracks), etc. Irreversible deformations, zones of adiabatic shear and microfractures are caused by these processes. Dynamic fracture is a complicated multistage process including an appearance, evolution and confluence of microdefects and a formation of embryonic microcracks, pores, their grow up to the break-up of a bodies with division into separate parts. The present paper include new results in the next scopes: 1) development the thermodynamically correct mathematical models of damageable thermoelastoviscoplastic medium (microfracture); 2) development the methods for determination of “nonstandart” constants of medium models, connected with microfracture of material; 3) numerical simulation of destruction (fragmentation) of constructions (macrofracture); 4) numerical investigation of some problems for damageable solids and structures (dynamical deforming and fracture of thick-walled cylindrical and spherical shells under explosion; dynamical deforming and fracture of thick-walled two-layer shell, filled with liquid, under impact and high velocity penetration; the problems of dynamic deforming and destruction of an oil-holding layer in gydraulic fracturing). Some of previously obtained results in consideration domains are published in the papers [1—5]. Russian Foundation for Basic Research (grants No. 06-01-00185 and No. 05-08-01435) and ISTC (grant No. 2992) are acknowledged for financial support.

The Space Debris Evolution Modeling Taking into Account Satellite’s Collisions

This paper is aimed at developing the techniques for mathematical modeling of long—term orbital debris evolution within the continual approach framework. The Russian Space Debris Prediction and Analysis (SDPA) model [1], [2], [3] is used as a basis of this study. Under this approach the equations of evolution contain some source terms responsible for variations of quantities of different fractions of orbital debris population caused by fragmentation and collisions. Our efforts were concentrated at determining the source terms for the equations of evolution, at developing the numerical—analytical technique for integrating the equations of evolution, which makes it possible to obtain the results within the reasonable time interval using modern PCs.