Micromechanics & Composites LLC

Centerville, OH, United States

Micromechanics & Composites LLC

Centerville, OH, United States

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Buryachenko V.A.,Micromechanics & Composites LLC
Computers and Structures | Year: 2017

We consider a linearly elastic composite material (CM), which consists of a homogeneous matrix containing a statistically homogeneous random set of noncanonical (i.e. nonellipsoidal) inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are different. One proposes a new exact representation for the first statistical moments of stresses in the phases expressed trough the averaged boundary integrals over the inclusion boundaries. These integrals presenting the perturbations introduced by a single inclusion inside the infinite matrix are evaluated by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. Increasing of volume fraction of inclusions can lead to change of a sign of local residual stresses estimated by either the new approach or the classical one. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D infinite domains containing statistically homogeneous random field of inclusions. © 2017 Elsevier Ltd


Buryachenko V.A.,Micromechanics & Composites LLC | Buryachenko V.A.,IllinoisRocstar, LLC
CMES - Computer Modeling in Engineering and Sciences | Year: 2012

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions modeling the morphology of heterogeneous solid propellants (HSP). Estimates of effective elastic moduli are performed using the multiparticle effective field method (MEFM) directly taking into account the interaction of different inclusions. Because of this, the effective elastic moduli of the HSP evaluated by the MEFM are sensitive to both the relative size of the inclusions (i.e., their multimodal nature) and the radial distribution functions (RDFs) estimated from experimental data, as well as from the ensembles generated by the method proposed. Moreover, the detected increased stress concentrator factors at the larger particles in comparison with smaller particles in bimodal structures is critical for any nonlinear localized phenomena for HSPs such as onset of yielding, failure initiation, damage accumulation, ignition, and detonation. Copyright © 2012 Tech Science Press.


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.


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.


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.


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.


Buryachenko V.A.,Micromechanics & Composites LLC
ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) | Year: 2015

In contrast to the classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175-209) is free of any spatial derivatives of displacement. The new general integral equations (GIE) connecting the displacement fields in the point being considered and the surrounding points of random structure composite materials (CMs) is proposed. For statistically homogemneous thermoperistatic media subjected to homogeneous volumetric boundary loading, one proved that the effective behaviour of this media is governing by conventional effective constitutive equation which is intrinsic to the local thermoelasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional thermoelasticity of CMs and adapted to thermoperistatics. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of decomposition of local fields into the load and residual fields similarly to the locally elastic CMs. This similarity opens a way for straightforward expansion of analytical micromechanics tools for locally elastic CMs to the new area of random structure peridynamic CMs. Detailed numerical examples for 1D case are considered. Copyright © 2015 by ASME.


Buryachenko V.A.,Micromechanics & Composites LLC
ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) | Year: 2015

One considers a linear heterogeneous media (e.g. filtra-tion in porous media, composite materials, CMs, nanocompos-ites, peristatic CMs, and rough contacted surfaces). The idea of the effective field hypothesis (EFH, H1, see for references and details [1], [2]) dates back to Mossotti (1850) who pioneered the introduction of the effective field concept as a local homo-geneous field acting on the inclusions and differing from the ap-plied macroscopic one. It is proved that a concept of the EFH (even if this term is not mentioned) is a (first) background of all four groups of analytical methods in physics and mechanics of heterogeneous media (model methods, perturbation methods, self-consistent methods, and variational ones, see for refs. [1]). An operator form of the general integral equations (GIEs) is ob-tained which connects the driving fields and fluxes in a point be-ing considered. New GIEs present in fact the new (second) back-ground (which does not use the EFH) of multiscale analysis of-fering the opportunities for a fundamental jump in multiscale re-search of random heterogeneous media with drastically improved accuracy of local field estimations (with possible change of sign of predicted local fields). Copyright © 2015 by ASME.


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.


Grant
Agency: Department of Defense | Branch: Navy | Program: SBIR | Phase: Phase I | Award Amount: 150.00K | Year: 2014

An accuracy of the classical"trial and error"testing method of the new Ceramic Matrix Composite (CMC) processes and constructions is no longer be affordable in modern industry and science. However, physics-based computational tools and methodologies which are needed to optimize these processes can"t provide a necessary accuracy without taking into account both the wide and detailed micromechanical modeling describing of microstructure evolution during processing as well as the final properties and performance in service. (i) propose and develop the linear and nonlinear micromechanical models of infiltration in the porous media consisting of random beds of cylinders; (ii) propose physics-based model for impregnation molding of particle-filled resin; (iii) propose and develop a dual scale porous medium containing two distinct scales of pores such as the fiber tows inside surrounding gaps. (iv) propose and develop the model of solidification with estimation of both the local stochastic residual stresses and effective failure envelope; (v) begin model validation by comparison to available CMC; and (vi) initiate implementation of the new model in software readily accessible to materials engineers.

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