#### 539.3 Asymptotic theory of constructive-orthotropic plates with two-periodic structures

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2014-1-3656

The theory of thin constructive-orthotropic plates with a two-periodic structure was suggested. Examples of such structures are honeycomb sandwich panels and backed plates. The theory is based on equations of a three-dimensional elasticity theory with the help of asymptotic expansions in terms of a small parameter being the ratio of a plate thickness and a characteristic length without introducing any hypotheses on a distribution character for displacements and stresses through the thickness. Local problems were formulated for finding stresses in all structural elements of a plate. It was shown that the global (averaged by the certain rules) equations of the plate theory are similar to equations of the

Dimitrienko Y., Gubareva E., Sborschikov S. Asymptotic theory of constructive-orthotropic plates with two-periodic structures. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 36-56

#### 539.3 Computational modeling and experimental investigation of elastic-plastic plates deforming under crushing

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Erasov V. S. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”), Yakovlev N. O. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”)

doi: 10.18698/2309-3684-2015-1-6782

The article presents a suggested method of numerical finite-element solving the ‘hole ovalization’ problem. This method can be applied for experimental development of advanced aviation materials with the aim of determining structure element resistance against deforming with stress concentrators, mainly, connectors. The method is based on three-dimensional finite element solution of the problem of lastoplastic deformation of plates with a hole under crushing. It is appropriate for reduction of xperimental studies and replacing them by the numerical experiments. The Ilyushin model of small lastoplastic deformations has been used. The results of numerical simulation of a threedimensional stress-strain state of elastoplastic plates under crushing are presented as well as results of experimental nvestigations of deforming plates of Al-alloy 163. It is shown that the results of numerical and experimental modeling for deforming plates under crushing agree quite well.

Dimitrienko Y., Gubareva E., Sborschikov S., Erasov V., Yakovlev N. Computational modeling and experimental investigation of elastic-plastic plates deforming under crushing. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 67-82

#### 539.3 Finite element modulation of effective viscoelastic properties of unilateral composite materials

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2014-2-2848

We propose a method for calculating effective viscoelastic properties of composite materials under steady-state cyclical vibrations. The method is based on asymptotic averaging of periodic structures and finite-element solution of local problems of viscoelasticity in periodicity cells of composite materials. We provide examples of numerical simulation of viscoelastic properties for composites with unidirectional reinforcement, and of calculations of complex tensors of stress concentration in a periodicity cell. The paper presents a comparative analysis of dependencies of loss tangent of complex composite elasticity
modulus on vibration frequencies obtained through FEA calculations and rough mixed formulae. We show that rough mixed formulae, often used for calculating dissipative properties of composite materials, can yield appreciable calculation errors.

Dimitrienko Y., Gubareva E., Sborschikov S. Finite element modulation of effective viscoelastic properties of unilateral composite materials. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 28-48

#### 539.3 Modeling the elastic-plastic characteristics of monocrystalline intermetallic alloys based on microstructural numerical analysis

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Bazyleva O. A. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”), Lutsenko A. N. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”), Oreshko E. I. (Federal State Unitary Enterprise “All-Russian Scientific Research Institute of Aviation Materials”)

doi: 10.18698/2309-3684-2015-2-322

The article presents a model of microstructure of two-phase monocrystalline intermetallic alloys in the form of a periodic structure of the hexagonal type, as well as a mathematical model of elastic-plastic deformation of monocrystalline alloy, based on the method of asymptotic smoothing periodic structures. Deformation plasticity theory under loading is used for the phases with due regard for the effect of their damage level during loading. For numerical calculations of the developed model the heat-resistant monocrystalline alloy of the type VKNA-1V was used. Finite element calculations of deformation and fracture micromechanical processes in monocrystalline alloy of the type VKNA-1V were carried out. It was found that under tension maximum values of phase damagability, which determine the beginning of the alloy micro-fracture zone, are achieved in the areas adjacent to the phase interface and in areas of maximum curvature of the geometric shape of the phases. Calculations of heat-resistant alloy strain diagrams in plastic range are proved to be consistent with experimental data.

Dimitrienko Y., Gubareva E., Sborschikov S., Bazyleva O., Lutsenko A., Oreshko E. Modeling the elastic-plastic characteristics of monocrystalline intermetallic alloys based on microstructural numerical analysis. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 3-22

#### 539.3+519.86 Multiscale modeling of elastic-plastic composites with an allowance for fault probability

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2016-2-323

The purpose of this article is to propose a model of deformation of elastic-plastic composite materials with periodic structures with an allowance for fault probability of the composite phases. The model is based on a variant of the deformation theory of plasticity with the active loading. To simulate the effective characteristics of elastic-plastic composites, we applied the method of asymptotic homogenization of periodic structures. For numerical solution of linearized problems on the periodicity cell we offered the finite elements method using SMCM software medium developed at the Scientific-Educational Center of Supercomputer Engineering Modeling and Program Software Development of the Bauman Moscow State Technical University. We provide the research with the examples of numerical computations for dispersion-reinforced metal composites (aluminum matrix filled with SiC particles). Finally, we present the results of numerical modeling of deformation processes, damage accumulation and metal-composite destruction.

Dimitrienko Y., Gubareva E., Sborschikov S. Multiscale modeling of elastic-plastic composites with an allowance for fault probability. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 3-23