Micromechanics & Composites LLC

Centerville, OH, United States

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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
ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) | Year: 2016

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. Either the volume integral equations or bound-ary ones are used for these GIEs, new concept of the interface polarisation tensors are introduced. New GIEs present in fact the new (second) background (which does not use the EFH) of multi-scale analysis offering the opportunities for a fundamental jump in multiscale research of random heterogeneous media with dras-tically improved accuracy of local field estimations (with possi-ble change of sign of predicted local fields). © Copyright 2016 by ASME.


Buryachenko V.A.,Micromechanics & Composites LLC
ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) | Year: 2016

One considers a linear elastic composite material (CM, [1] ), which consists of a homogeneous matrix containing the random set of heterogeneities. An operator form of the general integral equation (GIE, [2-6] ) connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions in the infinite media. The new GIE is presented in a general form of perturbations introduced by the heterogeneities and defined at the inclusion interface by the unknown fields of both the displacement and traction. 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, and some particular cases, asymptotic representations, and simplifications of proposed GIEs are presented for the particular constitutive equations of linear thermoelasticity. In particular, we use a meshfree method [7] based on fundamental solutions basis functions for a transmission problem in linear elasticity. Numerical results were obtained for 2D CMs reinforced by noncanonical inclusions. Copyright © 2016 by ASME.


Buryachenko V.A.,Micromechanics & Composites LLC
ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) | Year: 2016

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 homogeneous 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. A generalization of the Hills equality to peristatic composites is proved. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CMs are generalized to the case of peristatics, and the energetic definition of effective elastic moduli is proposed. 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 the decomposition of local fields into load and residual fields. Effective properties of thermoperistatic CM are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase. 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 © 2016 by ASME.


Buryachenko V.A.,Micromechanics & Composites LLC
Mathematics and Mechanics of Solids | Year: 2017

The basic feature of the peridynamic model considered here is a continuum description of a material's behavior as the integrated nonlocal force interactions between infinitesimal particles. In contrast to 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. A theory of thermoelastic composite materials (CMs) with nonlocal thermoperistatic properties of multiphase constituents of arbitrary geometry is analyzed for statistically homogeneous CMs subjected to homogeneous loading. A generalization of the Hill's equality to peristatic composites is proved. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CMs are generalized to the case of peristatics, and the energetic definition of effective elastic moduli is proposed. 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 the decomposition of local fields into load and residual fields. Effective properties of thermoperistatic CM are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase. A detected similarity of results for both the peristatic and locally elastic composites is explained fundamentally, as the methods used for obtaining the results widely exploit the Hill's condition and the self-adjointness of the stress operator. However, the representation of effective properties for composites with both the local thermoelastic and nonlocal thermoperistatic properties do not always coincide. Therefore, the representation of effective eigenfields through mechanical influence functions generalizing Levin's representation does not in general hold for thermoperistatic CMs; this is demonstrated for a one-dimensional numerical example. © SAGE Publications.


Buryachenko V.A.,Micromechanics & Composites LLC
International Journal of Solids and Structures | Year: 2017

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 (i.e. nonellipsoidal) shape. The new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals that makes it possible to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of ellipsoidal symmetry. The results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics. © 2017 Elsevier Ltd


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.,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.


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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