In this study, we investigated the possibility of determining the stiffness tensor using theoretical methods. We utilized a periodicity cell, not a representative elementary volume, to solve the problem, in which the periodicity of the inclusion center locations was considered. Three options were employed to estimate the effective deformation properties of composite materials with periodic inclusion center location arrangements and random size values. In this paper, the applicability of the proposed probabilistic approach to determining the effective stiffness tensor on a periodicity cell is shown. This approach allows one to obtain not only the mean values (i.e., the effective stiffness tensor) but also three main central moments-from the second to the fourth order-characterizing the random nature of the effective stiffness tensor. The approach developed and employed in this study to estimate the effective deformation characteristics of composite materials with periodic inclusion center location arrangements, characterized by random radii values, could be practically extended to other physical and mechanical properties.

Массовое использование композитов в машиностроении, авиакосмической технике, строительстве, расчеты зданий и сооружений с учетом совместной их работы с грунтами оснований, а также расчеты подземных сооружений и горных выработок совместно с вмещающим их массивом горных пород (грунты и горные породы по существу являются композитами природного образования) ставит задачу надежного, быстрого и удобного способа определения механических характеристик таких композитных материалов. В геомеханике определение механических свойств часто длительное по времени и весьма затратное, а иногда эти свойства невозможно определить экспериментальным путём. Таким образом, можно констатировать, что в настоящее время в инженерной и научной деятельности проблема определения эффективных характеристик композитных материалов является актуальной. Данная работа является продолжением исследований [1,2] по определению эффективного тензора жесткости и соответственно эффективных технических характеристик композитных материалов (модули Юнга, сдвига и коэффициенты Пуассона) с использованием вероятностных методов и метода асимптотического усреднения. Предлагаемый подход позволяет свести задачу по определению эффективных механических характеристик со случайными значениями характеристик фаз композитного материала к решению набора стандартных периодических задач на ячейке, не прибегая к рассмотрению представительного элемента объема. В отличие от предыдущих работ [1,2], где задача со случайным расположением включений [1] и случайными значениями размеров (радиусов) включений при условии соблюдения периодичности расположения их центров [2], в данной работе задача решается для композитов периодической структуры, но со случайными значениями их механических характеристик. В работе излагается четыре варианта оценки эффективных характеристик деформационных свойств композитных материалов периодической структуры со случайными значениями деформационных характеристик их фаз. Показана применимость предложенного вероятностного подхода к определению эффективного тензора жёсткости на ячейке периодичности. Такой подход позволяет получать не только средние значения (эффективный тензор жёсткости), но и три основных центральных момента - со 2-го по 4-й порядок (дисперсию, асимметрию и эксцесс), характеризующие случайную функцию распределения эффективного тензора жёсткости. Представленные в данной в статье подходы к оценке эффективных деформационных характеристик композитных материалов периодической структуры со случайными значениями механических характеристик могут быть применены к определению вязкоупругих, теплофизических и других физико-механических свойств.

автомобильной промышленности, в строительстве и машиностроении требует знания их механических характеристик. Также для расчетов связанных с производством геотехнических и горных работ необходимо определять механические свойства грунтов и горных пород, которые по существу являются композитами природного образования. Отметим, что в геомеханике определение механических характеристик часто трудоемко и весьма затратно, а для скальных грунтов экспериментальными методами, как правило, невозможно в силу ярко выраженного масштабного эффекта. Таким образом, определение механических характеристик композитных материалов является актуальной. Цель работы – определение тензора жесткости композитных материалов с периодическим расположением их центров и случайными значениями деформационных свойств аналитико-численными методами из решения задачи на ячейке периодичности, а не на представительном элементе объема. В работе рассматриваются различные варианты определения эффективных деформационных характеристик композитных материалов на примере композитных материалов со случайным коэффициентом Пуассона включения и случайным модулем упругости включения.

The presence of nanoeffects in polymer nanocomposites, which determine the properties of these nanomaterials, has been confirmed. In particular, these nanoeffects are the reason for the manifestation of identical properties in nano- and microcomposites with lower nanofiller content compared to microfillers. In turn, nanoeffects are attributable to a larger fraction of phase interfacial surfaces in the case of nanocomposites. Nanofiller aggregation reduces the properties of nanocomposites; in particular, it reduces their ability to generate interfacial regions.

Millimeter-wave (mmW) traveling-wave tube (TWT) devices are of interest for applications requiring amplifier output power in the >100 W range over instantaneous bandwidth of several GHz, but fabrication of the sub-wavelength slowwave structures has been a persistent challenge. We discuss the development of TWT device design and fabrication methods to advance the output power and bandwidth capability and improve the SWaP-C (size, weight, power, cost) of devices in the Ka-band to W-band frequency ranges.

It has been shown that graphene does not have any advantages over organoclay. The main characteristics of 2D nanofillers in a polymer matrix are not related to their initial properties. To realize the extremely high characteristics of polymer/2D nanofiller nanocomposites, it is necessary to create an optimal structure of the nanofiller in the polymer matrix. The aggregation degree and the aspect ratio of the tactoids of the 2D nanofiller are determined by the ratio of the nominal elasticity moduli of the nanofiller and the matrix polymer. The effective elasticity modulus of the nanofiller in the polymer matrix of the nanocomposite is determined by its rigidity.

When creating elastomeric composites, structures and products made from such materials, considerable attention is paid to environmental issues, as well as to improving economic efficiency and energy efficiency in its production. In this regard, the development of new types of strengthening highly dispersed fillers for elastomeric and polymer composite materials, including those of natural origin, providing an optimal balance of mechanical properties of composites and having advantages over existing solutions, is an actual task. In the course of the work, a technology was developed for producing highly dispersed fillers by ultrafine grinding of raw materials. The obtained experimental data shows a significant reinforcement effect (up to five times) with a decrease in the average particle size of the filler. It is established, that he most effective filler, in terms of reinforcement, are particles based on amorphous silicon dioxide, obtained from rice husk processing products and shungite rock. The significant influence of the surface functionality and the carbon/silicon dioxide ratio of submicron filler particles on the mechanical properties of elastomeric composites is shown. It is established that new classes of reinforcing fillers can be recommended for practical use in the future.

In this paper we use the method of asymptotic homogenization in parametric space to determine the effective properties of thermo-viscoelastic composite materials. These materials are composed of multilayered spherical inclusions imbedded in the matrix. In comparison with the traditional method of asymptotic homogenization, our approach allows for regular non-periodic distributions of inhomogeneities as well as dependences of the material characteristics on temperature. We start with the Laplace transform of the governing equations together with their boundary and initial conditions. To do so, we treat temperature and spatial coordinates responsible for non-periodic distribution of inclusions in the material as parameters (along with the parameter of Laplace transform itself). Then we define and implement a two-level scheme of asymptotic homogenization of the resulting equations in parametric space. At the first step, we solve the problem on the microscale level (a cell problem). At the second step, for the images of Laplace transform, we derive the macroscopic equation with effective coefficients. Finally, we perform the inverse Laplace transform to compute relaxation functions and determine thermo-viscoelastic properties of the composite material. The obtained results provide an information on how the change in properties and concentration of the inclusions affect the rheological characteristics and stress relaxation patterns for the thermo-viscoelastic composites.

Синтезированы и исследованы новые анизотропные силиконовые магнитоактивные композиты. Методом сканирующей электронной микроскопии определена структура поверхности и микроразмеры наполнителей из карбонильного железа этих эластомеров. Использование атомно-силовой микроскопии позволило определить значительные деформации поверхности и магнитострикционные эффекты при наложении небольших внешних магнитных полей на полученные композиты. Использование ядерного гамма резонанса позволило определить электронную конфигурацию железного наполнителя в этих анизотропных композитах.

In the paper, a two-level scheme is substantiated for representing solutions for thermoviscoelasticity equations with fast oscillating coefficients corresponding to a structurally inhomogeneous viscoelastic medium with nonlinear characteristics. In contrast to the traditional approach based on the classical method of asymptotic homogenization, here, in the analysis of the thermoviscoelasticity equations, additional nonlinear dependences of the material characteristics on temperature and on spatial coordinates are taken into account. To this end, the asymptotic homogenization procedure is formulated in such a way that the nonlinear dependences, which have a smoothly changing character against a background of fast oscillations of the coefficients, are resolved parametrically in the asymptotic analysis of the equations. As a result, a two-level scheme for representing solutions of thermoviscoelastic problems is formulated, which makes it possible to determine the effective rheological characteristics of a structurally inhomogeneous material and to obtain a stress relaxation pattern taking into account the internal microstructure.

Эластомерные композиты – перспективные конструкционные материалы, изделия из них применяются в автомобильной, авиационной, космической, нефтеперерабатывающей и др. промышленности. Основными компонентами в составе данного класса композитов являются эластомерная матрица и высокодисперсные частицы наполнителя, распределенные в объеме матрицы. Размеры данных включений могут варьироваться в широких пределах от нескольких десятков нанометров, до нескольких десятков микрон.

Abstract New silicone magnetoactive elastomers have been synthesized and studied. Significant magnetostrictive effects in the synthesized composites were visualized by microscopy. The obtained results can be the basis for the design of controlled dampers and promising magnetostrictive engines of a new generation with micro and nanoscale positioning accuracy and the ability to transmit significant force effects on the operated objects.

The relationship was studied between the parameter important for the formation of the properties of polymer nanocomposites, namely, the transfer efficiency of the mechanical stress applied to the sample from the polymer matrix to the nanofiller, and the structure of carbon nanotubes formed in this matrix. It has been found that the indicated efficiency, controlled by the level of interfacial adhesion of the nanofiller-polymer matrix, critically depends on the main negative process for all nanocomposites, that is, aggregation of the nanofiller, an increase in the degree which reduces the efficiency of stress transfer. For the nanocomposites under consideration, the process of carbon nanotubes aggregation takes place in the form of emergence of their annular formations that are fractal objects, which has been confirmed experimentally. This fact allows characterization of the carbon nanotubes structure in a polymer matrix using a fractal dimensionality. It has been found that an increase in the fractal dimensionality of the annular formations of carbon nanotubes, reflecting an upgrowth in the degree of their aggregation unambiguously reduces the efficiency of mechanical stress transfer as well as the nanofiller ability to generate interfacial regions.

In the present article, we argue a choice of a modifier (filler) for an epoxy binder, namely, carbon nanotubes. The solid-state epoxy adhesive obtained by modification is a 3-phase nanocomposite, where the matrix is epoxy resin, the filler is nanotubes, and the contact layer is the domain of the epoxy resin, molecules of which have been undergone conformation. Next, the effective deformation characteristics of such an epoxy adhesive have been determined using experimental and theoretical methods. We claim that the asymptotic averaging method, which is only one with rigorous mathematical justification, gives results being in a good agreement with experimental ones (discrepancy of ~3.4%).

An asymptotic averaging of differential equations with fast oscillating quasi-periodic coefficients so-called “the asymptotic averaging in parametric space” is developed. The system of equations corresponding to structurally heterogeneous thermoelastic media with smoothly varying microstructures is considered. Such materials are usually treated as functionally graded ones. Their description is satisfied by introducing two types of variables into the coefficients of the system of thermoelastic equations: “fast” and “slow”. The fast variables describe the geometry of the inhomogeneities provided their periodic arrangement. The additional variables allow one to describe a smooth spatial variation of a periodic structure of inclusions, i.e. to describe within the proposed approach various materials with functionally graded properties. In addition, the coefficients may depend on the temperature, which also has a given regular distribution in the space. The allocation of this dependence in the separate parameter makes sense, since it is important in practice. It is shown that the asymptotic averaging solves the smooth aperiodic dependencies for the coefficients of the considered equations system parametrically through the functions of rapid variables. A two-level model system for such structurally heterogeneous materials is formulated as a result of averaging, and an algorithm of accurate definition of thermomechanical properties including the functionally graded and thermally depending ones could be found. The combined numerical-analytical block method based on the Papkovich–Neuber​ representation is proposed for low-level problems with arbitrary structures (e.g. for the problem defined on a cell for functions of fast variables; such a problem determines the effective properties of a material). The structures with spherical and cylindrical inclusions and interphase layers are especially considered and the complete function systems allowing one an efficient solution approximation on a cell with exactly satisfied contact conditions on interlayers is constructed.

Carbon nanotubes represent a unique nanofiller with exceptional mechanical properties and a high degree of anisotropy. These characteristics determine the presence of two types of aggregation for such a nanofiller, namely, the formation of ropes (bundles) of individual nanotubes and formation of their annular structures. Estimates made within the percolation model have shown that each rope of carbon nanotubes in polyamide-6-based nanocomposites consists of several hundred individual nanotubes. In turn, the formation of such ropes has a critical effect on formation of annular structures of carbon nanotubes, since an increase in the diameter of ropes results in an increase in the radius of these annular structures. This effect determines both the level of interfacial adhesion in polymer nanocomposites and their final mechanical characteristics. It has been shown that an increase in the number of carbon nanotubes per one rope reduces its specific surface and the fractal dimensionality of the surface of ropes, which ultimately determines the decrease in the reinforcement degree of polymer/carbon nanotubes nanocomposites. The thermodynamic analysis of carbon nanotubes interactions has shown that these interactions are significantly higher than similar interactions between polymer macromolecules. This effect determines the formation of carbon nanotube ropes already at the stage of their production. The obtained results suggest that individual carbon nanotubes with a large radius of their annular structures can produce the greatest effect in reinforcement of polymer nanocomposites.

It is shown that the degree of crystallinity of the polymer matrix on introduction of dispersed nanoparticles is determined by the formation of crystallizing interfacial regions and the melting temperature of crystallites. Aggregation of the initial nanoparticles increases their effectiveness as a nucleating agent for crystallization of the polymer matrix. An increase in the degree of crystallinity of the polymer matrix fully explains the increase in the elasticity modulus in the case of polypropylene/calcium carbonate nanocomposites, and only partially of polypropylene/globular nanocarbon nanocomposites, due to the difference in the crystallization mechanism.