Rubric: "1.1.8. Mechanics of a Deformable Solid Body (technical sciences)"
Dimitrienko Y. I. (Bauman Moscow State Technical University), Salnikova A. A. (Bauman Moscow State Technical University), Oreshnikova E. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2023-4-4763
A mathematical model of phase transformations in steel alloys during resistance spot welding is proposed, taking into account all stages of the process: from heating and partial melting of the metal, which cause irreversible physical and chemical transformations of the steel microstructure, to the cooling stage, during which solidification and “return” formation of alloy phases occurs . The model describes changes in the 3D microstructure of a steel alloy during heating and subsequent cooling with the formation of ferritic and austenitic structures. An algorithm for calculating model constants using a special procedure for solving the inverse problem is proposed, as well as an algorithm for numerically solving the problem of predicting changes in the elastic properties of steel during the welding process, which includes finite element 3D modeling using the SMCM software package, developed at the Department of Computational Mathematics and Mathematics physics" of Bauman Moscow State Technical University. An example of numerical simulation using the proposed model and algorithm for a steel alloy is given.
Димитриенко Ю.И., Сальникова А.А., Орешникова Е.А. Моделирование изменения микроструктуры и упругих свойств сплавов в процессе контактной точечной сварки. Математическое моделирование и численные методы, 2023, № 4, с. 47–63
519.63 Modification of aluminum by laser shock wave detected in atomistic modeling
Perov E. A. (JIHT), Zhakhovsky V. V. (Dukhov Automatics Research Institute/JIHT), Алимович N. A. (L.D. Landau Institute for Theoretical Physics RAS), Shepelev V. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Fortova S. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Doludenko A. N. (JIHT)
doi: 10.18698/2309-3684-2023-4-7492
Plastic deformations are the basis of such industrial technology as laser thermal hardening or laser pinning (LSP, laser shock peening). In this paper, the possibility of hardening the surface layer of an aluminum sample irradiated by a single femtosecond laser pulse is investigated by the method of classical molecular dynamics. Several initialstates of the film are simulated; three orientations of the crystal lattice are investigated — [1, 0, 0] (the first orientation of the crystal lattice), [1, 1, 0] (the second orientation of the crystal lattice), [1, 1, 1] (the third orientation of the crystal lattice). A numerical study of the effect of various values of the invested energy in the range from 120,98 J/m2 to 2540,01 J/m2 of a laser pulse on the depth of plastic deformations affecting the hardening of the material under study was carried out. The energy values were selected in such a way that the plastic front of the UV (shock wave) stopped before it reached the right boundary of the simulated film. If this condition is not observed, then the dependence cannot be considered correctly constructed, since the stretching wave reflected from the right boundary of the sample will slow down the plastic shock front, acting as an unloading wave. With the help of this dependence, the threshold value of the invested energy is determined, when exceeded, aluminum begins to deform plastically.
Перов E.А., Жаховский В.В., Иногамов Н.А., Шепелев В.В., Фортова С.В., Долуденко А.Н.. Молекулярно-динамическое моделирование модификации алюминия лазерной ударной волной. Математическое моделирование и численные методы, 2023, № 4, с. 74-92
Belkheeva R. K. (Новосибирский государственный университет)
doi: 10.18698/2309-3684-2024-1-317
A model of the low-parameter equation of state of diamond was constructed, and the parameters of this equation were found, which allow to describe reliably the behavior of solid and porous diamond samples and diamond-metal mixture. Porous substance and porous mixture of condensed components were considered as thermodynamically equilibrium mixtures. The comparison of calculated and experimental shock adiabats showed the applicability of the proposed two-parameter equation of state in a wide range of pressures and temperatures.
Бельхеева Р.К. Моделирование малопараметрического уравнения состояния в форме Ми-Грюнайзена для алмаза и смесей алмаз-металл. Математическое моделирование и численные методы, 2024, № 1, с. 3–17.
Nikitin A. D. (Institute for Computer Aided Design of the Russian Academy of Sciences), Stratula B. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2024-1-1837
A comparative analysis of the fatigue strength of hot-rolled and SLM materials was performed based on data from high-frequency cyclic tests for corset specimens made of aluminum alloy D16T and SLM alloy AlSi10Mg on piezoelectric equipment. The relatively low cyclic strength of SLM materials is shown, which is associated with their complex microstructure and is influenced by the laser scanning strategy, laser beam parameters, energy, heat transfer from the melting zone, and environmental parameters in the chamber. Mathematical modeling of the process of fatigue failure of the specified specimens was carried out for various amplitudes and mean stresses in the cycle using a multi-mode model of cyclic damage and a numerical method for calculating the kinetics of damage under high-frequency cyclic loading. The proposed model and calculation method make it possible to quickly and efficiently fatigue curves constructing for various cyclic loading modes and cycle asymmetry coefficients. It is enough to know the base points of the bi-modal fatigue curve for the reverse cycle to implement this computational procedure.
Никитин А.Д., Стратула Б.А. Моделирование циклической повреждаемости и усталостной прочности при высокочастотном нагружении 3Д-напечатанных образцов из алюминиевого сплава. Математическое моделирование и численные методы, 2024, № 1, с. 18–37.
Dimitrienko Y. I. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University)
doi: 10.18698/2309-3684-2024-2-1734
The paper is devoted to modeling the deformation of composite materials with finite deformations. The so-called universal models of constitutive relations for composite components are considered, defining several classes of nonlinear relationship between the Piola-Kirchhoff stress tensor and the strain gradient within different energy pairs of stress-strain tensors. The method of asymptotic averaging is applied and local problems are formulated to solve the problem of determining the averaged properties of composites with finite deformations. A variational formulation of the original deformation problem, the so-called local problems on a periodicity cell and the averaged problem for a composite is considered, which makes it possible to use FEM for the numerical solution of these classes of problems. A software module has been developed as part of the SMCM software package, which implements the proposed numerical algorithm. An example of the numerical solution of problems on a periodicity cell for a 3D orthogonally reinforced composite is given, taking into account large deformations of the matrix and fibers, and composite deformation diagrams are calculated for various variants of universal models of constitutive relations.
Димитриенко Ю.И., Каримов С.Б., Димитриенко А.Ю. Моделирование конечных деформаций композиционных материалов на основе универсальных моделей Аn и метода асимптотического осреднения. Математическое моделирование и численные методы, 2024, № 2, с. 17–34.
Malinin V. G. (FSBEI HE «USTU»), Malinina N. A. (FSBEI HE «USTU»), Savich V. L. (FSBEI HE «USTU»), Malinin V. V. (Design Bureau of PJSC Tupolev), Askama P. A. (FSBEI HE Orel SAU), Otev K. S. (FSBEI HE «USTU»)
doi: 10.18698/2309-3684-2024-3-4364
A variant of the autowave model for generating structural imperfections when initiating localized plastic flow of crystalline bodies in a complex stress state is considered, based on the methods of the structural and analytical theory of strength and the principles of synergetics of the elastoplastic deformation process. The formulated model takes into account the development of processes at two interrelated scale and structural levels, allows us to predict the features of elastoplastic deformation of crystalline materials with complex loading trajectories in stress space and arbitrary stress change programs over time, takes into account the effects of localization and relaxation of energy in structural concentrators on the processes of self-oscillation of zones of structural concentrators during elastoplastic deformation.
Малинин В. Г., Малинина Н. А., Савич В. Л., Малинин В. В., Аскама Пенья А., Отев К. С. Структурно–аналитическая модель пластической деформации, учитывающая автоволновые процессы генерации дефектов. Математическое моделирование и численные методы, 2024, № 3, с. 43–64.