Dimitrienko

pp. 296-312

pp. 216-233

pp. 748-770

pp. 359-382

pp. 243-265

A mathematical model of deformation of flexible armored materials based on aramid fabric under high-speed effects was proposed. The model takes into account the following peculiarities of deformation parameters of composite materials of the specified class: possibility of deformation without destruction at finite deformations, a considerable difference between stress-deformation diagrams under tension and under compression, dependence of these diagrams on a loading rate, pseudo-plastic features of materials caused by pulling out threads from fabric and/or a plastic character of deformation, anisotropy of nonlinear-elastic and visco-plastic properties and other effects. A problem statement was formulated for dynamic deformation of flexible armored materials. In order to solve the problem in a two-dimensional case the method of band-adaptive grids was applied. An example of numerical solution of the problem was presented for a high-speed action of a striker onto a flexible armored material; some effects of deformation of materials of the specified class were analyzed.

Using a multi-scale homogenization method, a three-level model was developed for ceramic composite materials based on the reaction-bonded SiC. Numerical simulation was performed with the use of the finite-element method for solving a set of local problems over the periodicity cells of three structural levels. Tensor fields of stress concentration were computed in matrices and fillers. A new strength criterion of a matrix and fillers at multi-axis stress state was applied; this criterion takes into account a significant difference (more than ten times) between strength features of ceramics under tension and compression. A model that takes into account a scale effect of the strength of ceramic composites was proposed. Numerical investigation of sequential microstructural destruction of ceramic composites up to the final fracture was conducted. Computations demonstrated that at the presence of a polydisperse structure of ceramics, a change in concentrations of large-scale fractions plays less considerable role than in the case of small particles fraction.

A mathematical multi-level model for calculating thermo-elastic properties of textile composites with alumino-chromic phosphate matrices under high temperatures was developed. This model takes into account physical-chemical transformations occurring in an alumino-chromic phosphate binder and glass fibers under a high temperature. Comparison of calculation results with experimental data was carried out; it was shown that the developed model allowed to predict a complicated nonlinear character of changes in elastic properties of composites under heating up to 1600 К. The developed model could be used for prediction of elastic properties of composites with alumino-chromic phosphate matrices under complicated heating modes.

In this paper, the authors presented a mathematical model for calculating effective dielectric characteristics of complex structured composite materials influenced by an external alternating electric field. An asymptotic investigation of electro-dynamic differential equations with fast oscillating coefficients was carried out. A local electro-dynamic problem on the composite’s “periodicity cell” was formulated. An effective complex permittivity of composite materials with various volume fractions of the fine-dispersed ferroelectric ceramic inclusions was calculated by the finite element method and the biconjugate gradient stabilized method. The authors analyzed frequency dependence of dielectric characteristics and dielectric loss tangent of composite ceramics. The obtained results are good congruous to experimental data.

In this paper the authors formulated a problem of optimising the composite micro-structure, which is a problem of minimisation of the composite density under given restrictions on the components of effective elasticity and heat-conduction tensors, and effective limits of the composite strength. The authors proposed a method for solving an optimal design problem of a composite material reinforced with micro-spheres and designed for thermal shielding. The method of asymptotical averaging (homogenisation method) was used for calculating effective composite characteristics such as elastic and heat-conduction modulus tensors and strength limits; the finite element method was used for solving local 3D heat conduction and elasticity theory problems on the composite’s periodicity cells. The finite element method was implemented with the use of GCD software developed at “FN-11” department of Bauman MSTU. The Hooke Jeeves algorithm was used for solving optimisation problems. Numerical implementation of the proposed method of micro-structure optimisation was developed by the example of a composite based on glass micro-spheres.

In this article the authors propose a finite-element method for calculating non-stationary heat-mass-transfer 3D problems in heat-shielding structures made of composite materials with consideration for thermo-decomposition and filtration of gases in pinholes. Specialized software that implements the numerical finite-element method for solving the problem of internal heat-mass-transfer in 3D elements of structures made of composite thermo-destructive materials was developed. In this paper the authors also present results of testing the developed method and software that illustrate working capacity of this method and its applicability to solving investigation problems of non-stationary heating modes of heat-shielding structures.

In this paper, the authors consider calculation of effective dielectric parameters of composite materials with complex three-dimensional armoring. The method of asymptotic averaging of periodic structures is used for averaging of long-term quasi-static electric fields in composites with dielectric components. Series of local electrostatic tasks were formulated with the use of periodicity cells; electrostatic variational problems were also formulated. To solve spatial local problems for composite materials with three-dimensional complex armoring, the finite element numerical method was used. In this article, the authors proposed an algorithm for computation of effective tensor of dielectric permeability of three-dimensional armored composite materials. Test computations were carried out in order to obtain distribution of the local electric field, effective dielectric characteristics of three-dimensional orthogonal armored composite materials with different inclusion volume fractions.

In this work a method of microstructural finite element analysis for calculation of strength surface of composite materials with periodic fabric structure of reinforcement on the basis of a developed software was proposed. This method is a method of asymptotic averaging adapted for multi-scale periodic structures developed by Prof. Y. Dimitrienko at the "Computational Mathematics and Mathematical Physics" department. The method is based on solving a special class of elasticity problems on 1/8th of the periodicity cell of the composite in order to determine effective elastic properties of the material. The results of calculation of ultimate strength for disperse reinforced and textile composites are presented.

The authors consider problems of modeling processes in new types of damping devices, in which the working fluid is a two-phase system: a porous body -  a fluid which does  not wet it. On the basis of the theory of heterogeneous porous systems with phase changes they propose a mathematical model of non-stationary processes in a heterogeneous working fluid damper. Specific tasks for calculating micro-and macro parameters of the damping system are formulated. Numerical methods for solving these problems are developed.