Materials physics and mechanics

RAR RUS 1-4 Pierre and Marie Curie University Rajchenbach

Paris, France

Stress Transmission through a Cohesionless Material We apply a point load onto a bidimensional packing of elastic grains. The internal state of stress is accessed by means of photoelastic visualization. The region in which the stress response is confined exhibits a parabolic profile. This evidence supports the parabolic nature of the equations describing the stress transmission. Our results oppose classical elasto-plastic models of continuum mechanics, and other recent hyperbolic proposals. Cohesionless Material; Stress Transmission https://mpm.spbstu.ru/article/2001.4.1/ 2001_3_1_p1.pdf

RAR RUS 5-11 University of Manchester Institute of Science and Technology Harris

Manchester, UK

A Model for the Flow of Granular Materials and its Application to Initial/Boundary Value Problems A plasticity type model is here considered for the flow of a dry granular material such as grain or sand. The physical and kinematic basis for the model is briefly summarised and the equations governing the model are presented in terms of the components of the deformationrate, spin and stress tensors. The equations comprise a set of six first order partial differential equations of hyperbolic type for which there are five distinct characteristic directions. An idealised application to a hopper is considered for the flow in the vicinity of the upper free surface. A simple analytic solution is given in which (a) the velocity field is linear in the space coordinates and represents a dilatant or contractant shear, (b) two possible stress fields are proposed, one linear and one exponential in space, which satisfy the stress equilibrium equations, the yield condition and the traction-free condition at the free surface, (c) the density is homogeneous in space and exponential in time. Finally, a method is proposed for defining an intrinsic time-scale for the deformation, which enables a physically realistic density field to be obtained via a sequence of dilatant and contractant shearing motions. Full advantage is taken of the hyperbolic nature of the governing equations to allow the solution to have discontinuities in the field variables, or their derivatives, in crossing characteristic lines. Granular Materials; Plasticity type model https://mpm.spbstu.ru/article/2001.4.2/ 2001_3_1_p2.pdf

RAR RUS 12-20 Delft University of Technology Askes

Delft, The Netherlands

Delft University of Technology Suiker

Delft, The Netherlands

Delft University of Technology Sluys

Delft, The Netherlands

Dispersion Analysis and Element-Free Galerkin Simulations of Higher-Order Strain Gradient Models The role of strain gradients in continuum mechanics has been studied. Distinction is made between stabilizing and destabilizing gradients. A combined model is proposed to investigate the interaction of the two effects. Dispersion analysis and numerical simulations are used to compare the various formats of the model in a qualitative and a quantitative manner. It is shown that a destabilizing second-order gradient has a devastating effect on the numerical response, even if a stabilizing second-order gradient is present. For this class of models only the absence of destabilizing terms guarantees convergent numerical responses. Higher-Order Strain Gradient Models Element-Free Galerkin Simulations https://mpm.spbstu.ru/article/2001.4.3/ 2001_3_1_p3.pdf

RAR RUS 21-24 K-4577-2013 57384230400 St.Petersburg State University Petrov Yuri y.v.petrov@spbu.ru

St.Petersburg, Russia

Institute of Problems of Mechanical Engineering RAS Brigadnov

St.Petersburg, Russia

Institute of Problems of Mechanical Engineering RAS Freidin A.B.

St.Petersburg, Russia

Institute of Problems of Mechanical Engineering RAS Indeitsev

St.Petersburg, Russia

7005573911 St.Petersburg State University Morozov N.F.

St.Petersburg, Russia

Energy Estimations of Phase Transformations under the Action of a Spherically Converging Compression Wave A model for description of the deformation processes initiated by phase transformations in a ball subjected to the action of a spherically converging compression wave of high power is proposed. Explanation for the effect of cavity origination in the center of a ball is given. Phase Transformations Energy Estimations Spherically Converging Compression Wave https://mpm.spbstu.ru/article/2001.4.4/ 2001_3_1_p4.pdf

RAR RUS 25-35 Martin Luther University of Halle-Wittenberg Altenbach

Halle, Germany

A Non-Classical Model for Creep-Damage Processes The analysis of creep-damage processes is becoming more and more important in engineering practice due to the fact that the exploitation conditions like temperature and pressure are increasing while the weight of the structure should decrease. In the same time the safety standards are increasing too. The accuracy of the mechanical state estimation (stresses, strains and displacements) mainly depends on the introduced constitutive equations and on the chosen structural analysis model. For the first purpose an improved generalized phenomenological creep model is introduced and extended to the case of creep-damage coupling. In addition, a micromechanical-based model is discussed. For thin-walled structures under creep-damage conditions the advantages and the problems of different approaches are briefly discussed. Creep-Damage Processes Non-Classical Mode https://mpm.spbstu.ru/article/2001.4.5/ 2001_3_1_p5.pdf

RAR RUS 36-44 Institute of Problems of Mechanical Engineering RAS Aero

St.Petersburg, Russia

Catastrophic Microdeformations in Crystalline Lattice. Structure Stability and Modifications Essentially nonlinear theory of three-dimensional lattice subjected to the intensive shear is presented. Two, acoustic and pseudo optical, branches of deformations are considered. The deformation energy is shown to consist of periodic and gradient terms. The equilibrium equation in the sine-Helmholtz form is exactly solved. It demonstrates some effects of bifurcations. The first effect is the transformation of homogeneous macrodeformation into inhomogeneous one, in which case a superstructure with large periods and a new translation order are formed. The second bifurcation effect is associated with occurrence of two deformed, elastic and elastoplastic, states, in which case the short-range atomic order is altered and a new modification of crystalline lattice is formed. Some criteria of local and global structural stability are revealed. Microdeformations Crystalline Lattice https://mpm.spbstu.ru/article/2001.4.6/ 2001_3_1_p6.pdf

RAR RUS 45-51 Peter the Great St. Petersburg Polytechnic University Krivtsov

St.Petersburg, Russia

University of Aberdeen Wiercigroch

Aberdeen, UK

Mechanical Properties of Polycrystal Materials, Molecular Dynamics Simulation The lack of continuity conditions of the rock materials presents a serious challenge for the continuum mechanics approach, hindering the effective use of the well-established methods such as the finite element method and the boundary element methods. In the presented paper a discrete technique based on molecular dynamics approach is used for computer constructing of polycrystal materials. On the first step material grains are obtained from condensation of vaporised mixture of particles. Then the grains are compressed to obtain the material with the desirable porosity. Another variant for obtaining polycrystals is melting of the grain mixture with the consequent cooling. Uniaxial compressive loading tests for the obtained computer materials are presented, where the stress-strain relationships for mono and polycrystal specimens are compared. Influence of porosity on elastic and strength properties of the material is investigated. Applications for sandstone materials with different porosity are considered. Use of the described technique for simulation of percussive drilling in hard rock formations is discussed. Polycrystal Materials Molecular Dynamics Simulation https://mpm.spbstu.ru/article/2001.4.7/ 2001_3_1_p7.pdf

RAR RUS 52-56 Institute of Fundamental Technological Research Wojnar

Warsaw, Poland

Dynamic Growth of a Spherical Inclusion in Thermoelastic Medium The paper deals with an initial value problem of dynamic uncoupled thermoelasticity concerning a moving spherical thermal inclusion in an infinite solid. An extended Kosevich' theory of continuously distributed defects due to prescribed plastic fields is used. Applying a generalization of the isothermal elastodynamics with continuosly distributed defects, the displacement and stress fields due to a spherical thermal inclusion growing linearly with time are obtained. Spherical Inclusion Thermoelastic Medium Dynamic Growth https://mpm.spbstu.ru/article/2001.4.8/ 2001_3_1_p8.pdf

RAR RUS 57-61 University of Seville Castellanos

Seville, Spain

University of Seville Sánchez

Seville, Spain

University of Seville Valverde

Seville, Spain

The Onset of Fluidization in Xerographic Toners An estimation of the dominant stresses in powders with or without interstitial gas flow yields a semiqualitative criteria for the transition between flow regimes (plastic-fluidized, plasticinertial, plastic-suspension, inertial-fluidized, inertial-suspension). It will be shown that, at ambient pressure, fine powders (particle diameter less than ~ 100 µm) experience a direct transition from plastic to fuidized regime, or from plastic to suspension. The inertial regime is absent in these fine powders. These ideas will be applied to understand the onset of fluidization in rotating drums. Previous measurements with xerographic toners (particle diameter around 10 µm) in rotating drums indicated that fluidized and plastic regimes coexist in the drum. The extent of the fluidized region grows when angular speed is increased. Here, we present measurements on the width of the horizontal surface of the fluidized zone as a function of rotation velocity, drum diameter and toner properties. We find that the results depend on the product of three fundamental parameters: (i) the ratio of the fluidized toner bulk density to the packed toner bulk density; (ii) the ratio of centrifugal acceleration to the acceleration of gravity and (iii) the ratio of gravitational potential energy per unit volume (or equivalently, kinetic energy per unit volume) to the powder tensile strength. Xerographic Toners Fluidization https://mpm.spbstu.ru/article/2001.4.9/ 2001_3_1_p9.pdf

RAR RUS 63-100 Institute of Problems of Mechanical Engineering RAS Meshcheryakov Yu.I.

St.Petersburg, Russia

Institute of Problems of Mechanical Engineering RAS Divakov

St.Petersburg, Russia

Institute of Problems of Mechanical Engineering RAS Zhigacheva

St.Petersburg, Russia

Role of Mesostructure Effects in Dynamic Plasticity and Strength of Ductile Steels Dynamic deformation and fracture of solids are known to be the multiscale processes. Mesolevel-1 relates to deformation modes inside the structure elements while mesolevel-2 is self-consistent motions of conglomerates of the elements. Shock experiments and molecular dynamics simulation show a presence of local strain rate fluctuations (dispersion) which sensitively depend on the non-equilibrium of deformation process. Velocity dispersion at the mesolevel-1 (D2 m1) characterizes a relaxation of local stresses while the dispersion at the mesolevel-2 (D2 m2) is responsible for fragmentation of material. When Dm1 = Dm2 fragmentation is suppressed and material reveals maximum strength. At the unsteady stages of straining the particle velocity acquires defect of velocity which characterizes an intensity of energy exchange between scale levels. In the present paper the energy exchange is considered from the position of spallation. For five kinds of steel it is shown that spall-strength is maximum when the velocity dispersion at the mesolevel equals defect of the average velocity. Criterion for spallation takes into account the energy exchange between scale levels. Steels Plasticity Strength Mesostructure https://mpm.spbstu.ru/article/2001.4.10/ 2001_3_1_p10.pdf

RAR RUS 101-107 Institute of Chemistry of the Komi Science Center, Ural Division of RAS Ryabkov

Syktyvkar, Russia

Institute of Chemistry of the Komi Science Center, Ural Division of RAS Istomin

Syktyvkar, Russia

Saint-Petersburg State University Chezhina

St.Petersburg, Russia

Structural Design and Properties of Layered Nanocomposite Titanium Carbide-Silicide Materials The titanium carbide-silicide Ti3SiC2 phase with crystal lattice formed by alternative structural blocks with the block thickness in the order of 1 nm, for the first time, is fabricated by the method based on the carbo-thermal reduction of titanium and silicon oxides and high temperature processing of titanium carbide in SiO vapors. It is experimentally revealed that the Ti3 SiC2 compound (treated as a layered nanocomposite) ehxibits the unique combination of properties which are non-typical for conventional ceramic materials. In particular, the crystal structure and chemical transformations showed an increase in the paramagnetic component of magnetic susceptibility, which can be attributed to titanium (III). It is found that the titanium carbide-silicide phase with layered structure has antiferromagnetic properties. The well-known method of magnetochemical control over the state of paramagnetic atoms in oxygen lattices is applied, for the first time, to titanium carbide-silicide phase. The obtained data can be used as the basis of a new method to control either the formation of layered titanium carbide-silicide phase or the gaseous silicon monoxide content in various physical and chemical processes. Titanium Carbide-Silicide Materials Nanocomposite Structural Design https://mpm.spbstu.ru/article/2001.4.11/ 2001_3_1_p11.pdf

RAR RUS 108-112 Institute of Problems of Mechanical Engineering RAS I.A. Ovid’ko И.А.

St.Petersburg, Russia

Physical Mechanisms of Reduction of Critical Current Density across Grain Boundaries in High - Tc Superconductors The combined effects of dilatation stresses, stoichiometric and electric-charge inhomogeneities, dx 2 -y2 symmetry of the superconducting order parameter and the faceted microstructure of grain boundaries are theoretically examined here as those causing the experimentally observed (see, e.g., Dimos et al, Phys.Rev. B 41 (1990) 4038) reduction of the critical current density Jc across grain boundaries in high-Tc cuprates. The enhancement of Jc across high-quality twist and doped grain boundaries in high-Tc cuprates is briefly discussed. High - Tc Superconductors Grain Boundaries Critical Current Density https://mpm.spbstu.ru/article/2001.4.12/ 2001_3_1_p12.pdf