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Centerville, OH, United States

Buryachenko V.A.,Micromechanics & Composites LLC
Engineering Analysis with Boundary Elements | Year: 2016

One considers linearly elastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical shape. Effective elastic moduli as well as the first statistical moments of stresses in the phases are estimated through the averaged boundary integrals over the inclusion boundaries. The modified popular micromechanical models are based on the numerical solution for one inhomogeneity inside the infinite matrix loaded by remote homogeneous effective field. This solution is obtained by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. The problem here addressed, consists in computing the displacement and traction fields of an elastic object, which has piecewise constant Lamé coefficients, from a given displacement (or stress) field on the infinity. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D domains. © 2015 Elsevier Ltd.All rights reserved. Source


Buryachenko V.A.,University of Akron | Buryachenko V.A.,Micromechanics & Composites LLC
International Journal for Multiscale Computational Engineering | Year: 2015

One considers a slow linear flow through a fixed random bed of rigid particles. The general integral equations (GIEs) connecting the fields of velocities and pressures of fluid in a point being considered and the fields in the surrounding points are obtained for the random (statistically homogeneous and inhomogeneous, so-called graded) structures containing the particles of arbitrary shape and orientation. The new GIEs are presented in a general form of perturbations introduced by the heterogeneities. The mentioned perturbations can be found by any available numerical method which has advantages and disadvantages; if it is crucial for the analyst to be aware of their range of applications. The method of obtaining GIEs is based on a centering procedure of subtraction from both sides of a new initial integral equation, their statistical averages obtained without any auxiliary asymptotic assumptions, which are exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs and establishes an advantage with the known GIEs. © 2015 by Begell House, Inc. Source


Buryachenko V.A.,University of Akron | Buryachenko V.A.,Micromechanics & Composites LLC
International Journal for Multiscale Computational Engineering | Year: 2015

One considers a linear composite medium, which consists of a homogeneous matrix containing either the periodic or random set of heterogeneities. An operator form of the general integral equation (GIE) is obtained for the general cases of local and nonlocal problems, static and wave motion phenomena for composite materials with periodic and random (statistically homogeneous and inhomogeneous, so-called graded) structures containing coated or uncoated inclusions of any shape and orientation with perfect and imperfect interfaces and subjected to any number of coupled or uncoupled, homogeneous or inhomogeneous external fields of different physical nature. The GIE, connecting the driving fields and fluxes in a point being considered and the fields in the surrounding points, are obtained for both the random and periodic fields of heterogeneities in the infinite media. The new GIE is presented in a general form of perturbations introduced by the heterogeneities and taking into account a possible imperfection of interface conditions. The mentioned perturbations can be found by any available numerical method which has advantages and disadvantages and it is crucial for the analyst to be aware of their range of applications. The method of obtaining of the GIE is based on a centering procedure of subtraction from both sides of a new initial integral equation their statistical averages obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs which are presented in two equivalent forms for both the driving fields and fluxes. Some particular cases, asymptotic representations, and simplifications of proposed GIE are presented for the particular constitutive equations such as linear thermoelastic cases with the perfect and imperfect interfaces, conductivity problem, problems for piezoelectric and other coupled phenomena, composites with nonlocal elastic properties of constituents, and the wave propagation in composites with electromagnetic, optic, and mechanical responses. © 2015 by Begell House, Inc. Source


Buryachenko V.A.,University of Akron | Buryachenko V.A.,Micromechanics & Composites LLC
International Journal for Multiscale Computational Engineering | Year: 2015

The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated nonlocal force interactions between discrete material points. A statistically homogeneous heterogeneous bar of random structure of constituents with thermoperistatic mechanical properties is analyzed by using the standard averaging tool of micromechanics for the linear thermoelastic media. We demonstrate the applicability of the local thermoelasticity theory for the description of effective behavior of this bar. The mentioned analogy between the numerical models for the thermoelastic and termoperistatic heterogeneous bars is explained by the general results establishing the links between the effective properties (effective elastic moduli and effective thermal expansion) and the corresponding mechanical and transformation influence functions. The approach proposed is based on a numerical solution (for both the displacements and peristatic stresses) for one heterogeneity inside an infinite homogeneous bar loaded by either a pair of self-equilibrated concentrated remote forces or the residual stresses. These solutions are substituted into the general scheme of micromechanics of locally thermoelastic media adapted for the considered case of 1D thermoperistatic structures. One demonstrates a convergence of effective property estimations obtained for the thermoperistatic composite bar to the corresponding exact effective properties evaluated for the local thermoelastic theory. In so doing, the results obtained show that the thermoperistatic theory predicts some features that would not be presented in the classical linear thermoelastic solution. Thus, the effective eigenstrain exactly predicted in the classical local theory does not depend (in the 1D case) on the elastic properties of constituents, whereas this effective parameter evaluated in the thermoperistatic theory does depend on the micromoduli of constituents. © 2015 by Begell House, Inc. Source


Buryachenko V.A.,University of Akron | Buryachenko V.A.,Micromechanics & Composites LLC
International Journal of Solids and Structures | Year: 2014

One considers a linear composite materials (CM), which consists of a homogeneous matrix containing a random set of heterogeneities. An operator form of solution of the general integral equation (GIE) for the general cases of local and nonlocal problems, static and wave motion phenomena for composite materials with random (statistically homogeneous and inhomogeneous, so-called graded) structures containing coated or uncoated inclusions of any shape and orientation with perfect and imperfect interfaces and subjected to any number of coupled or uncoupled, homogeneous or inhomogeneous external fields of different physical nature. The GIE, connecting the driving fields and fluxes in a point being considered and the fields in the surrounding points, are obtained for the random fields of heterogeneities in the infinite media. Estimations of the effective properties and both the first and second statistical moments of fields in the constituents of CMs are presented in a general form of perturbations introduced by the heterogeneities and taking into account a possible imperfection of interface conditions. The solution methods of GIEs are obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known methods of micromechanics. Some particular cases, asymptotic representations, and simplifications of proposed methods are presented for the particular constitutive equations such as linear thermoelastic cases with the perfect and imperfect interfaces, conductivity problem, problems for piezoelectric and other coupled phenomena, composites with nonlocal elastic properties of constituents, and the wave propagation in composites with electromagnetic, optic and mechanical responses. © 2014 Elsevier Ltd. All rights reserved. Source

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