Asymptotic models and transport properties of densely packed, high-contrast fibre composites. Part I: Square lattice of circular inclusions

Andrianov, Igor V.; Awrejcewicz, Jan; Starushenko, Galina A.

doi:10.1016/j.compstruct.2017.07.070

Cited by 10 publications

(8 citation statements)

References 20 publications

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“…3. For obtaining the effective parameter 𝑞 𝑦 , integration in expression ( 13) is performed over the original region of the hexagonal cell, taking into account relation (26), that is, 𝐴 2 , 𝐵 2 , 𝐶 2 are treated as functions of 𝜉.…”

Section: Solving a Cell Problem By Thin Layer Asymptoticsmentioning

confidence: 99%

“…This paper stands as a continuation of the series of works devoted to the application of AHM to the fibre-reinforced composites of various structures (square [26][27][28], hexagonal [27,28,[30][31][32]) and various type of inclusions (circular [26,27,[30][31][32], square [29], rhombic [27] and curvilinear rhombic [27]). A distinctive feature of these works relates on the analytical solving of the cell problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

Andrianov

Awrejcewicz

Starushenko³

et al. 2022

Z Angew Math Mech

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Paper is devoted to the effective stationary heat conductivity for the fibre composite materials. We are aimed on getting on analytical expression for effective thermal conductivity coefficient. Asymptotic homogenization approach, based on the multiple scale perturbation method, is used. This allows to reduce the original boundary value problem in multiply connected domain to the sequence of boundary value problems in simply connected domains. These problems include: the local problem for the periodically repeated cell and homogenized problem with effective coefficient. It is shown that for densely packed and high contrast fibre composites, the cell problem can be solved analytically. For this aim, lubrication approach (asymptotics of thin layer) has been employed. We also generalise obtained solution to the case of medium‐sized inclusions in the framework of the Padé approximants.

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Section: Solving a Cell Problem By Thin Layer Asymptoticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

Andrianov

Awrejcewicz

Starushenko³

et al. 2022

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

“…The first solution in (13) has no physical meaning, because the Poisson's ratio is always not larger than 1/2.…”

Section: Critical Exponents In Traditional Emtmentioning

confidence: 99%

“…for an arbitrary large ratio of Young's modulus of the first and second phases. Although in the real-world composites ideal periodic structures do not occur, analytical results for the elastic moduli of ordered structures are useful because they allow one to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly employed for control engineering of composite-material-based systems [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

2020

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It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity-theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magneto-elastic properties of magnetorheological elastomers, as it has been achieved for magneto-dielectric and magnetic properties recently.

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“…Focussing on fibre-reinforced composites, Andrianov et al (2017) considered an infinitely thin interface on the phase boundary, the properties of which are the average value of the properties of the matrix and fibres. This interface model model was used to derive the effective asymptotic formulae for conductivity of densely packed fibre-reinforced composites, including the case of non-conducting fibres contacting each other through a thin conducting interface.…”

Section: Introductionmentioning

confidence: 99%

Hashin’s bounds for elastic properties of particle-reinforced composites with graded interphase

Sburlati

Cianci

Kashtalyan

2018

International Journal of Solids and Structures

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The paper is focused on analytical prediction of the effective bulk and shear modulus for particulate composites reinforced with solid spherical particles surrounded by graded interphase zone. A three-dimensional elasticity problem for a single inclusion embedded in a finite matrix is studied. The graded interphase zone around the inclusion is assumed to have power law variation of the shear modulus with radial coordinate , with Poisson's 1 ratio assumed to be constant and equal to that of the matrix. Following Hashin's approach, two boundary value problems are considered and stress and displacement fields in the interphase zone are determined. They are then used to calculate the elastic energy for the single inclusion composite under spherically symmetric state and pure shear state and derive closed-form expressions for the bulk modulus and the upper and lower bounds for the shear modulus. Numerical results for hard and soft interphase zones are presented and discussed for a range of the interphase zone thickness ratios.

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Asymptotic models and transport properties of densely packed, high-contrast fibre composites. Part I: Square lattice of circular inclusions

Cited by 10 publications

References 20 publications

Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

Hashin’s bounds for elastic properties of particle-reinforced composites with graded interphase

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