Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Buryachenko, Valeriy A.

doi:10.21203/rs.3.rs-2066623/v1

Cited by 3 publications

(5 citation statements)

References 57 publications

(106 reference statements)

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“…The analysis of clustered CMs, where the aligned hierarchical clusters contain some anisotropic layers, is straightforward. At last multiphysics and nonlinear problems (see for references [20,23,24,49]) of peridynamic micromechanics are also the possible area for expansion of this method. It should be mentioned that for locally elastic multilayer CM [24], one proved that effective moduli are identical for both the periodically placed layers and MT estimations of randomly placed layers.…”

Section: Discussionmentioning

confidence: 99%

Generalized Mori-Tanaka Approach in Peridynamic Micromechanics of Multilayered Composites of Random Structure

Buryachenko

2024

J Peridyn Nonlocal Model

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The basic feature of the peridynamics is a continuum description of material behavior as the integrated nonlocal force interactions between material points. Besides the conventional local theory, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175--209) has no spatial derivatives of displacement. A linearized bond-based peridynamic model is used for the analysis of random structure CMs subjected to the remote volumetric homogeneous boundary conditions. Effective properties are expressed through the local stress polarization tensor averaged over the external interaction interface of inclusions rather than in an entire space. Any spatial derivatives of displacement fields are not required. Inclusions are considered as identical aligned layers with a statistically homogeneous distribution in the space. For one infinite layer in the infinite homogeneous matrix, 3D peridynamic equilibrium equation is reduced to the 1D integral equation with 1D micromodulus obtained by integrations of the original 3D micromodulus over the cross-sections (parallel to layers) of a horizon region. One estimates the average strain and stress fields in the extended layer by the use of averaging displacement and traction over the external interaction interface. Effective moduli for peridynamic multilayered CM are estimated in the matrix form representations usually used in locally elastic multilayered CM and based on the consideration of the normal and tangential parts of the effective moduli matrix.

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Section: Discussionmentioning

confidence: 99%

Generalized Mori-Tanaka Approach in Peridynamic Micromechanics of Multilayered Composites of Random Structure

Buryachenko

2024

J Peridyn Nonlocal Model

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Section: Discussionmentioning

confidence: 99%

Generalized Mori-Tanaka approach in peridynamic micromechanics of multilayered composites of random structure

Buryachenko¹

2022

Preprint

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The basic feature of peridynamics is a continuum description of material behavior as the integrated nonlocal force interactions between material points. Besides the conventional local theory, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175-–209)has no spatial derivatives of displacement. A linearized bond-based peridynamic model is used to analyze random structure CMs subjected to the remote volumetric homogeneous boundary conditions. Effective properties are expressed through the local stress polarization tensor averaged over the external interaction interface of inclusions rather than in an entire space. Any spatial derivatives of displacement fields are not required. Inclusions are considered as identical aligned layers with a statistically homogeneous distribution in the space. For one infinite layer in the infinite homogeneous matrix,3D peridynamic equilibrium equation is reduced to the 1D integral equation with 1D micromodulus obtained by integrations of the original 3D micromodulus over the cross-sections (parallel to layers) of a horizon region. One estimates the average strain and stress fields in the extended layer by the use of averaging displacement and traction over the external interaction interface. Effective moduli for peridynamic multilayered CM are estimated in the matrixform representations usually used in locally elastic multilayered CM and basedon the consideration of the normal and tangential parts of the effective moduli matrix.

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“…However, when plastic deformations happen, the homogeneity of the mechanical properties of the phases is lost and the local properties of the individual phases become position-dependent. A local theory of elastoplastic deformation of random structure CMs was proposed in [46] (see also [5, 10, 47]) in the framework of flow theory and small elastoplastic strains. We will consider a generalization of this theory by implementing the clustered discretization approach of CSA.…”

Section: Fta and Sca In Analytical Micromechanics Of Random Structure...mentioning

confidence: 99%

“…Due to estimation of D cJI by the use of the FEA, see sections 3 and 4, (rather than the Green's function technique (25)), there are no difficulties for the analysis of any anisotropy of the comparison moduli L c at the iteration effective moduli L * [n+1] (101) mentioned in Liu et al [27]. Thus, the effective stiffness L * defined by equation (13 1 ) can be estimated by three different formulae (47) (through the strain concentration factors A I , I = 1, . .…”

Section: Estimation Of Effective Moduli Through the Eigenstress Inter...mentioning

confidence: 99%

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Transformation field analysis as a background of clustering discretization methods in micromechanics of composites

Buryachenko¹

2023

Mathematics and Mechanics of Solids

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A linear composite material (CM) consisting of a homogeneous matrix with either the periodic or random set of heterogeneities is considered. One of the first reduced-order models (ROMs), Transformation Field Analysis (TFA) by Dvorak for the pair strain-eigenstrain (or stress-eigenstress) is modified in terms of the “mixed” pair strain-eigenstress (or stress-eigenstrain) for implementation to clustering-based ROMs initiated by the self-consistent clustering analysis (SCA) by WK Liu. A set of consistency conditions are obtained for both the effective properties and modified eigenfield concentration factors. It is found that modified TFA represents a unified background of all three central clustering-based ROMs: the SCA, virtual clustering analysis (VCA), and finite element analysis–clustering analysis (FCA). One presents the scheme of estimation of inhomogeneous strain concentration factors in some prescribed clusters analyzed by the SCA (nonlinear problem). For statistically homogeneous CMs, a localized version of the modified TFA is proposed for clustering of the matrix (coating) in the vicinity of inclusions. VCA used for the analysis of a finite size inclusion can be modified for the implementation of a combination of both the modified TFA and functional gradient theory.

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Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Cited by 3 publications

References 57 publications

Generalized Mori-Tanaka Approach in Peridynamic Micromechanics of Multilayered Composites of Random Structure

Generalized Mori-Tanaka Approach in Peridynamic Micromechanics of Multilayered Composites of Random Structure

Generalized Mori-Tanaka approach in peridynamic micromechanics of multilayered composites of random structure

Transformation field analysis as a background of clustering discretization methods in micromechanics of composites

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