Materials physics and mechanics

RAR RUS 1-7 Peter the Great St. Petersburg Polytechnic University Zisman

St.Petersburg, Russia

Element-free numerical modeling with discrete gradient and its application to crystal defects The gradient operation has been extended to discrete data in terms of nodal coordinates. On this ground, the nodal strains and related stresses are expressed directly in terms of nodal displacements and the stress divergence in terms of nodal stresses. To make use of truly discrete modeling in computational solid mechanics, the stress balance equation is formulated. For a case study, the latter is applied to an edge dislocation where atom positions of a dislocated crystal are taken for nodal points. Both the resulting stress level at the dislocation core close to the theoretical strength and the corresponding core dimensions prove to be realistic physically, whereas the long-range nodal stresses asymptotically approach the virtual continuous fields known in an analytical form. 10.18720/MPM.4512020_1 discrete gradient edge dislocation element-free model shape function stress balance https://mpm.spbstu.ru/article/2020.78.1/ 1-Alexander-A_-Zisman.pdf

RAR RUS 8-19 Peter the Great St. Petersburg Polytechnic University Vasilyev

St.Petersburg, Russia

Peter the Great St. Petersburg Polytechnic University Sokolov

St.Petersburg, Russia

Peter the Great St. Peresburg Polytechnic University Sokolov

St.Petersburg, Russia

Modeling microstructure evolution during thermomechanical processing and heat treatment of steels and predicting their mechanical properties An integral computer model/program AusEvol Pro was developed to describe the evolution of steel microstructure during thermomechanical processing (hot rolling, forging), as well as subsequent heat treatment (normalization, tempering), and to evaluate the final mechanical properties (yield stress, tensile stress, elongation), hardness and impact toughness. The program implements a set of physically based models that allow quantitative description of all significant processes of steel structure formation with account of the effects of chemical composition both during thermomechanical processing and heat treatment. Calculations of the final mechanical properties are carried out using the developed models that take into account all physically meaningful contributions. The models created are verified both on the extensive database of our own experimental studies and on reliable data from literature for steels of various chemical compositions. 10.18720/MPM.4512020_2 heat treatment mechanical property microstructure modeling steel thermomechanical processing https://mpm.spbstu.ru/article/2020.78.2/ 2-A_A_-Vasilyev-et-al.pdf

RAR RUS 20-30 Peter the Great St. Petersburg Polytechnic University Mamchits

St.Petersburg, Russia

Peter the Great St. Petersburg Polytechnic University Nemov Alexander

St.Petersburg, Russia

Peter the Great St. Petersburg Polytechnic University Karandashev

St.Petersburg, Russia

Baltico GmbH Büchler

Hohen Luckow, Germany

Baltico GmbH Vasilyev

Hohen Luckow, Germany

Baltico GmbH Ignatiev

Hohen Luckow, Germany

Development of a composite hatch cover Two designs of a composite marine hatch cover were developed on the basis of the design of a steel one. One of the proposed designs features composite structure made by means of manual lay-up technology, and the other one is based on a truss composite structure which can be produced by rod winding process. Selection of the most rational materials and design parameters was carried out on the basis of finite element simulations and use of parametric optimization methods. Results reveal the possibility of weight reduction by means of using composites in the hatch cover, which is associated, however, with a comparatively high cost. 10.18720/MPM.4512020_3 composite material finite element analysis hatch cover parametric optimization sandwich panel https://mpm.spbstu.ru/article/2020.78.3/ 3-D_-Mamchits%2C-A_-Nemov%2C-A_-Karandashev%2C-D_-Buechler%2C-R_-Vasilyev%2C-M_-Ignatiev(1).pdf

RAR RUS 31-37 Peter the Great St. Petersburg Polytechnic University Leontiev

St.Petersburg, Russia

Ulyanovsk State University Efremenkov

Ulyanovsk, Russia

3D finite element, connected with orthogonal finite functions, in modeling and investigation of elastic homogeneous and heterogeneous materials A novel 2D finite element (FE) associated with orthogonal finite functions (OFF, orthogonal splines) was developed for the ANSYS software and was tested early. The expansion of this method is presented here. The novel 3D FE, connected with 3D OFF is proposed for modeling and investigation of the stress-strain state of homogeneous and heterogeneous elastic bodies. The accuracy of the solutions obtained with this 3D FE is as high as for the classic ANSYS 3D FE. The developed 3D FE requires significantly less computational time; the winning of computational time increases with the amount of FE in a model. 10.18720/MPM.4512020_4 3D finite element homogeneous material heterogeneous materials orthogonal finite function shape function https://mpm.spbstu.ru/article/2020.78.4/ 4-V_L_-Leontiev-and-I_V_-Efremenkov(1).pdf

RAR RUS 38-48 Peter the Great St. Petersburg Polytechnic University Melker A.I.

St.Petersburg, Russia

Institute of Continuous Media Mechanics (RAS) Matveenko V.P.

Perm, Russia

Natural isomers of fullerenes from C4 to C20 We have systematized possible ways of forming the isomers of mini-fullerenes, namely elementary fullerenes: tetrahedron C4, triangular prism C6, cube C8, pentagonal prism C10, hexagonal prism C12, as well as their derivatives, which were obtained by joining elementary fullerenes. Combined with the graph analysis, this approach allows obtain a clear knowledge of their structure. Among them there are barrel-shaped fullerenes: C12, C16, C20; tetrahedral ones C12 and C16; bi-shamrocks C14 and C18, bipyramids C14 and C18; regular and irregular dodecahedrons C20 as well as intermediate compounds. The three simplest elementary fullerenes, C4, C6, C8; have only electronic isomers and no space atomic isomers at all. After a cube, the next in size carbon fullerene C10 is a pentagonal prism. We have designed an isomer of it by fusion of a tetrahedron and a triangular prism. For the pentagonal prism shape fullerene the energy lies in the range from 974 to 2464 kJ/mol, for the hybrid of a tetrahedron and a triangular prism does in the range from 1396 to 2433 kJ/mol; it depends both on the number of single and double bonds as well as on their position in space. Fullerene of twelve carbon atoms C12 produces four isomers: a hexagonal prism, a barrel-shape fullerene, a truncated tetrahedron and a tetra-penta octahedron. They have different energies depending on the number of single and double bonds and their position in space. In a like manner other fullerenes studied, C14, C16, C18 and C20, have two or three isomers with different energies. 10.18720/MPM.4512020_5 atomic isomer electronic isomer energy fullerene fusion reaction graph representation growth periodic system https://mpm.spbstu.ru/article/2020.78.5/ 5-Alexander-I_-Melker-and-Aleksandra-N_-Matvienko(1).pdf

RAR RUS 49-59 Peter the Great St. Petersburg Polytechnic University Melker A.I.

St.Petersburg, Russia

Institute of Continuous Media Mechanics (RAS) Matveenko V.P.

Perm, Russia

Natural isomers of fullerenes from C20 to C28 We have systematized possible ways of forming the isomers of midi-fullerenes, namely C22, C24, C26 and C28. There are three the most natural mechanisms of their obtaining: embedding carbon dimers into initial fullerenes; fusion of carbon cupolas having the same symmetry; fusion of fullerenes having compatible symmetry. The minimum energy fullerenes are obtained through the use of the first mechanism. It is worth noting that these fullerenes conserve the topological three-fold symmetry. At the same time the graph representation shows the change of symmetry from three-fold symmetry to six-fold one. Combined with the graph analysis, this geometric modeling allows obtain a clear knowledge of the structure of the fullerenes formed. 10.18720/MPM.4512020_6 atomic isomer electronic isomer energy fullerene fusion reaction graph representation growth periodic system https://mpm.spbstu.ru/article/2020.78.6/ 6-Alexander-I_-Melker-and-Aleksandra-N_-Matvienko(1).pdf

RAR RUS 60-78 Peter the Great St. Petersburg Polytechnic University Melker A.I.

St.Petersburg, Russia

Institute of Continuous Media Mechanics (RAS) Matveenko V.P.

Perm, Russia

Peter the Great St. Petersburg Polytechnic University Krupina

St.Petersburg, Russia

Natural isomers of fullerenes from C30 to C40 We have systematized possible ways of forming the isomers of midi-fullerenes, namely C30, C32, C34 C36, C38 and C40. Similar to the isomers of midi-fullerenes from C20 to C28, there are three the most natural mechanisms of their formation: 1) Embedding carbon dimers into initial fullerenes; 2) Fusion of carbon cupolas having the same symmetry; and 3) Fusion of fullerenes having compatible symmetry. The energies of the fullerenes calculated through the use of molecular mechanics are presented together with their graphs. It is found that in the majority of cases the minimum-energy fullerenes are those, having perfect and topological three-fold symmetries. 10.18720/MPM.4512020_7 atomic isomer dimer embedding energy fullerene fusion reaction graph representation growth periodic system self-organization symmetry topological symmetry https://mpm.spbstu.ru/article/2020.78.7/ 7-Alexander-I_-Melker%2C-Aleksandra-N_-Matvienko-and-Maria-A_-Krupina(1).pdf

RAR RUS 79-86 Department of Mathematics, U A M Sánchez-Bernabe

Mexico

Towards a periodic pattern in classical and nonclassical fullerenes with tetrahedral structure We have considered the following classical fullerenes: C40 C84 and C92. All of them have tetrahedral symmetry. The nonclassical fullerenes C64 and C76 were proposed earlier. Now, we have outlined a constructive process to obtain both fullerenes. The Table obtained earlier is complemented with four nonclassical fullerenes C52, C60, C88, and C100. The mass difference Δm between the numbers of carbon atoms of the fullerenes forms the sequence: 8, 4, 12, 8, 4, 12, 8, 4, 12. Its periodicity has no gaps as before. 10.18720/MPM.4512020_8 isolated pentagon rule nonclassical fullerene Schlegel diagram tetrahedral symmetry https://mpm.spbstu.ru/article/2020.78.8/ 8-F_J_-Sanchez-Bernabe(1).pdf

RAR RUS 87-95 Peter the Great St. Petersburg Polytechnic University Bezrukova

St.Petersburg, Russia

Peter the Great St. Petersburg Polytechnic University Vlasova

St.Petersburg, Russia

Nano- and microparticle aggregation: unique optical vectors for control The multiparameter analysis of simultaneous optical data for systems of nano- and/or micro-particles (3D disperse systems, dispersions, colloids, ensembles with the average diameter less than 10 micrometers) can be presented as the system characteristics characterized by N-dimensional unique vectors of optical parameters that can elucidate changes in the state of system particles. The application of ND unique optical vector approach is shown for several biomedical dispersions at the processes of aggregation. This approach can serve as the online control platform for the management of technological processes with 3D disperse systems. 10.18720/MPM.4512020_9 absorbance aggregation biomedical nano and micro particle light scattering ND optical vector 3D disperse system https://mpm.spbstu.ru/article/2020.78.9/ 9-Alexandra-G-Bezrukova-and-Olga-L-Vlasova(1).pdf

RAR RUS 96-100 Peter the Great St. Petersburg Polytechnic University Sanin

St.Petersburg, Russia

Simple Wigner-Langevin equation A new dynamical equation is derived by substituting the Schrödinger-LangevinKostin equation into the definition for the Wigner function, it can be called the quantumclassical Wigner-Langevin equation. The proposed equation contains partial derivatives for time and phase space variables of the Wigner function, its coefficients are spatial derivatives of potentials that take into account friction, white noise and external influence. The transition to the classical regime of motion is also discussed. 10.18720/MPM.4512020_10 phase space Wigner-Langevin quantum-to-classical transition friction white noise https://mpm.spbstu.ru/article/2020.78.10/ 10-Andrey-L_-Sanin(1).pdf

RAR RUS 101-103 A. S. Pushkin Brest State University Sery

Brest, Republic of Belarus

Influence of resonance Compton scattering in a magnetic field on rotation of the polarization plane of photons The solution of the problem of the value of rotation of photon polarization plane in totally spin-polarized electron gas in quantizing magnetic field is obtained. The second order perturbation theory on electromagnetic coupling is considered using modified Gell-Mann– Goldberger–Thirring dispersion relationship and optical theorem. Approximate formula obtained by Fomin and Kholodov for resonance Compton scattering cross-section is used in calculation. 10.18720/MPM.4512020_11 Baryshevsky–Luboshits effect electron gas quantizing magnetic field spin polarization of electrons https://mpm.spbstu.ru/article/2020.78.11/ 11-Alexey-I_-Sery(1).pdf

RAR RUS 104-131 B.I. Stepanov Institute of Physics Ivashkevich

Minsk, Belarus

Mozyr State Pedagogical University Ovsiyuk

Mozyr, Belarus

Belarus State University of Informatics and Radio-electronics Kisel

Minsk, Republic of Belarus

B.I. Stepanov Institute of Physics Red'kov

Minsk, Belarus

Spinor Maxwell equations in Riemannian space-time and the geometrical modeling of constitutive relations in electrodynamics It is known that vacuum Maxwell equations being considered on the background of any pseudo-Riemannin space-time may be interpreted as Maxwell equations in Minkowski space but specified in some effective medium, which constitutive relations are determined by metric of the curved space-time. In that context, we have considered de Sitter, anti de Sitter, and Schwarzschild models. Also we have studied hyperbolic Lobachevsky and spherical Riemann models, parameterized by coordinates with spherical or cylindric symmetry. We have proved that in all the examined cases, effective tensors and of electric permittivity and magnetic permeability obey one the same condition: . Expressions for tensors and are simple, but this simplicity is misleading. For each curved space-time model we are to solve Maxwell equations separately and anew. We have constructed the solutions, applying Maxwell equations in spinor form. 10.18720/MPM.4512020_12 constitutive relations electrodynamics geometrical modeling Maxwell equations Riemannian space-time spherical and cylindric symmetry spinor formalism https://mpm.spbstu.ru/article/2020.78.12/ 12-A_V_-Ivashkevich%2C-E_M_-Ovsiyuk%2C-V_V_-Kisel%2C-V_M_-Red%E2%80%99kov(1).pdf

RAR RUS 132-149 Peter the Great St. Petersburg Polytechnic University Melker A.I.

St.Petersburg, Russia

Nuclear geometry: from hydrogen to boron Possible ways of nuclear synthesis in the range from hydrogen to boron are studied. The geometric model of these nuclei is suggested. The basis for this model is the analogy between tetrahedral fullerene C4 and helium 2He4 . It is assumed that a nucleus of helium 2He4 has the form of a tetrahedron, where: 1) All the apices are equivalent and therefore they are protons, 2) Each neutron in a nucleus decomposes into a proton and three negatively charged particles having the charge ⅓ of that of an electron, 3) Interaction of the negative particles creates a special electronic pattern, which symmetry does not coincide with that of protons one, but determines it. On the basis of the postulates, the structure of other nuclei has been designed using geometric modeling. For hydrogen, deuterium, tritium and helium 3, a point, a linear and a plane structure respectively have been obtained. Helium 4 has tetrahedral symmetry. Then there was transition from three-fold symmetry prisms (lithium 6 and 7) to five-fold symmetry (boron 10 and 11) through four-fold one (beryllium 8, 9, 10). The nuclear electron patterns are more complex; their polyhedrons resemble the electron pairs arrangement at the valence shells of molecules. 10.18720/MPM.4512020_13 beryllium boron deuterium graph representation helium hydrogen lithium nuclear electron nuclear geometry https://mpm.spbstu.ru/article/2020.78.13/ 13-Alexander-I_-Melker(1).pdf

RAR RUS 150-166 Peter the Great St. Petersburg Polytechnic University Melker A.I.

St.Petersburg, Russia

Nuclear isomers and isotopes of carbon The nuclear geometry has been developed by analogy with the fullerene geometry. On the base of this geometric approach, the structure of carbon isomers and isotopes, which can be obtained by means of nuclear synthesis, has been designed. The mechanisms of possible nuclear reaction are discussed. Carbon is an unusual element. It has four isomers of different symmetry: three-fold, six-fold and tetrahedral ones, two being stable and one halfstable. The isotopes of carbon inherit the structure of the isomers. 10.18720/MPM.4512020_14 carbon graph representation isomer isotope nuclear electron nuclear geometry nuclear reaction nuclear synthesis https://mpm.spbstu.ru/article/2020.78.14/ 14-Alexander-I_-Melker(1).pdf