Rubric: "1.1.8. Mechanics of a Deformable Solid Body (physical and mathematical sciences)"
539.3 Modeling the deformation of layered periodic composites based on the theory of plastic flow
Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Черкасова М. С. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-2-1537
The aim of this work is to find the constitutive relations for a layered elastoplastic composite according to the flow theory using the method of asymptotic averaging. This goal is achieved by developing an algorithm for solving the problem of the theory of plastic flow for a layered composite material, taking into account various characteristics and properties of these layers of the material, followed by visualizing the result in the form of effective plasticity diagrams connecting the components of averaged stress tensors and components of averaged strain tensors.
Димитриенко Ю.И., Губарева Е.А., Черкасова М.С. Моделирование деформирования слоистых периодических композитов на основе теории пластического течения. Математическое моделирование и численные методы, 2021, № 2, с. 15–37.
Valishin A. A. (Bauman Moscow State Technical University), Tinyaev M. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-1-4262
When designing products made of composite materials intended for use in difficult conditions of inhomogeneous deformations and temperature, it is important to take into account viscoelastic, including spectral and dynamic, properties of the binder and fillers. The article considers dynamic characteristics (complex modulus, complex malleability,their real and imaginary parts, loss angle tangent) and spectral characteristics of relaxation and creep and their dependence on each other. The characteristics mentioned above were found for all known types of creep kernel and relaxation kernel. To find the spectral characteristics, one of the numerical methods of inverting the Laplace transform was used — the method of quadrature formulas with equal coefficients. Algorithms and computer programs for the implementation of this method have been compiled. The obtained graphs are quite accurate (the maximum error of calculations in the average does not exceed 5%), despite the fact that the error is very noticeable in the initial time segments.
Валишин А.А., Тиняев М.А. Моделирование динамических и спектральных вязкоупругих характеристик материалов на основе численного обращения преобразования Лапласа. Математическое моделирование и численные методы, 2022, № 1, с. 42–62.
Stratula B. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2021-4-4557
A unified numerical method for different fatigue fracture modes from low-cycle to very-high-cycle fatigue is described on the basis of a multi-mode two-criterion model of cyclic damage. This method allows for a through calculation of the evolution of crack-like fatigue fracture zones in a material, as well as an assessment of the durability of specimens from crack nucleation to macrofracture. Fatigue fracture calculations of titanium alloy specimens under prolonged cyclic loading under three-point bending scheme with development of "quasi-cracks" in modes from multi-cycle to super-multi-cycle fatigue have been carried out. Numerical and experimental results are compared to each other.
Стратула Б.А. Математическое моделирование усталостного разрушения при высокочастотных изгибных колебаниях образцов из титановых сплавов. Математическое моделирование и численные методы, 2021, № 4, с. 45–57.
Golovina N. Y. (Industrial University of Tyumen)
doi: 10.18698/2309-3684-2023-1-331
This article is the third part of a review of works devoted to the study of the properties of elastic-plastic materials. The first and second parts were devoted to the analysis of universal empirical laws of deformation, which model the material properties over the entire range of deformation, up to fracture. It was concluded that in order to create a model of the material response to stress growth, the deformation law must be at least four-parametric. The empirical Ramberg-Osgood law was found to be the most qualitative, at least for the titanium alloy VT6 considered. However, despite its accuracy, it does not reflect the material properties in the zone of large plastic strains, including in the vicinity of the point of ultimate strength. This paper presents an analysis of multilink models describing the relationship between strain and stress by different laws in the elastic zone and in the plastic zone. The review includes two-link models by Nadai, Mirambell-Real, Rasmussen, Abdella, formulated for materials whose strain curve has no positive curvature section. Also considered in the review are the three-link models of Quach; Hertele; Belov-Golovina, which allow modeling of deformation curves with a positive curvature region. The evaluation of the quality of empirical laws and their correspondence to the sample of experimental points was carried out by minimizing the standard quadratic deviation and using the method of gradient descent to determine the minimum of the function of many variables. The material for the comparative analysis of empirical models is titanium alloy VT6; for the Hertele and Belov-Golovina models — steel St3sp. It is shown that the models built on the basis of multi-line splines determine the properties of elastic-plastic materials more accurately than the models built on the basis of universal laws.
Головина Н.Я. Анализ эмпирических моделей кривых деформирования упруго-пластических материалов (обзор). Часть 3. Математическое моделирование и численные методы, 2023, No 1, с. 3–31.
539.3 Asymptotic theory of thin multilayer micropolar elastic plates
Dimitrienko Y. I. (Bauman Moscow State Technical University), Boyko S. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2023-2-3366
The problem of development of a theory for calculating the stress-strain state of thin multilayer elastic plates in the moment (micropolar) theory, is considered. The solution of this problem is built using an asymptotic analysis of the general equations for a 3-dimensional quasi-static problem of the moment theory of elasticity. The asymptotic analysis is carried out with respect to a small parameter representing the ratio of the plate thickness to its characteristic length. Recurrent formulations of local problems of the moment theory of elasticity are obtained. Explicit analytical solutions are obtained for these problems. The derivation of the averaged system of equations for multilayer plates is presented. It is shown that the asymptotic theory makes it possible to obtain an explicit analytical expression for all 9 components of the stress tensor and the moment stress tensor (in general) in the plate. As a special case, the problem of calculating the stress-strain state of a centrally symmetrical hingedly fixed plate when bending under the action of a uniformly distributed pressure. A complete analytical solution of this problem for all non-zero components of the stress tensor and the moment stress tensor is obtained. A numerical analysis of the solution of the problem for a single layer plate for the stress tensor is carried out, basing on the obtained expressions. A comparative analysis of the obtained results with similar calculations for the classical theory of elasticity is carried out, with revealing of similarities and differences for all components of the stress tensor.
Димитриенко Ю.И., Бойко С.В. Асимптотическая теория многослойных тонких микрополярных упругих пластин. Математическое моделирование и численные методы, 2023, № 2, с. 33–66.
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
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.
Dimitrienko Y. I. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University)
doi: 10.18698/2309-3684-2024-3-1842
The problem of developing a universal criterion for long-term fatigue strength of isotropic materials, in which the accumulation of damage differs significantly under loading in the region of tension and compression, is considered. Usually, to model the durability of such materials, Goodman diagrams are used, which take into account the dependence of durability on the load asymmetry coefficient. However, this model, as a rule, contains only one so-called S-N curve, as a result of which the fatigue life curves at different asymmetry coefficients turn out to be self-similar, which is not always observed in experimental data. In addition, Goodman diagrams are only applicable for cyclic loading. This article proposes a further development of the “chemical” criterion, which was previously developed in the author’s works, and which is applicable for a wide range of loads, both long-term static and cyclic with a random form of the loading cycle. The development of the “chemical” criterion for fatigue strength was carried out by separately taking into account the accumulation of damage in the areas of tension and compression. For mixed loading modes in the tension-compression region, a special layer accumulates damage in the tension and compression areas. A method for determining the constants of the proposed fatigue life model has been developed. It is shown how Goodman diagrams are constructed for the developed version of the fatigue life criterion. An example of using the “chemical” criterion to simulate the fatigue life of 34CrNiMo6 steel is considered.
Димитриенко Ю.И., Димитриенко А.Ю. «Химический» критерий для моделирования усталостной долговечности материалов, разносопротивляющихся растяжению-сжатию. Математическое моделирование и численные методы, 2024, № 3, с. 18–42.