A rigorous analytical method for doubly periodic cylindrical inclusions under longitudinal shear and its application

Jiang, Chunxiang; Xu, Yuzhe; Cheung, Y.K.; Lo, S.H.

doi:10.1016/s0167-6636(03)00010-3

Cited by 45 publications

(26 citation statements)

References 19 publications

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“…Table 1 presents the normalized effective elastic modulus C * 44 /C (1) 44 , for perfect contact (K = 10 12 ) computed by the present model using AHM, the Finite Element Method proposed in this work and the results reported in Jiang et al [20]. The material parameters used for this calculation are C (2) 44 /C (1) 44 = 120 for Table 1 Effective elastic modulus obtained by Jiang et al [20], AHM-uniform interface and FEM for composites with perfect contact, square and hexagonal periodic cell and ratio (C (2) 44 /C (1) hexagonal and square periodic cell. Table 2 shows the behavior of the effective longitudinal shear elastic modulus C * 44 = C * 55 for the same arrangement of the periodic cell obtained by Jiang et al [20], the present model by AHM for void volume fraction (K = 10 −12 ) and the Finite Element Method.…”

Section: Analysis Of Resultsmentioning

confidence: 98%

“…The material parameters used for this calculation are C (2) 44 /C (1) 44 = 120 for Table 1 Effective elastic modulus obtained by Jiang et al [20], AHM-uniform interface and FEM for composites with perfect contact, square and hexagonal periodic cell and ratio (C (2) 44 /C (1) hexagonal and square periodic cell. Table 2 shows the behavior of the effective longitudinal shear elastic modulus C * 44 = C * 55 for the same arrangement of the periodic cell obtained by Jiang et al [20], the present model by AHM for void volume fraction (K = 10 −12 ) and the Finite Element Method. The matrix shear modulus used is C (1) 44 = 30 GPa.…”

Section: Analysis Of Resultsmentioning

confidence: 99%

“…Some previous studies also reported the elastic effective coefficients for two-phase fibrous composites with rhombic array of periodic cells, both with perfect and with imperfect contact conditions, analytically and numerically [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of fibrous elastic composites with nonuniform imperfect adhesion

et al. 2015

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In most composites, the fiber-matrix adhesion is imperfect; the continuity conditions for stresses and displacements are not satisfied. In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method (AHM), for three-phase fibrous composites (matrix/mesophase/fiber) with parallelogram periodic cell. Interaction between fiber and matrix is considered, and this is called the mesophase model where the nonuniform mesophase is studied. Besides, there is another type of 1 matrix-fiber contact which is called nonuniform spring imperfect contact. In this case, the contrast or jump of the displacements in the boundary of each phase is proportional to the corresponding component of the tension in the interface in terms of a parameter given by a certain function that depends on the position. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The three-phase model is validated by the Finite Element Method and the AHM both approaches applied to two-phase composites with nonuniform spring imperfect contact. Comparisons with theoretical and experimental results verified that the present model is efficient for the analysis of composites with presence of nonuniform imperfect interface and parallelogram cell. The effect of the nonuniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.

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Section: Analysis Of Resultsmentioning

confidence: 98%

Section: Analysis Of Resultsmentioning

confidence: 99%

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Analysis of fibrous elastic composites with nonuniform imperfect adhesion

et al. 2015

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“…Among the works on the analytical solution, the representative ones that should be mentioned are those of Nemat-Nasser and Hori (1993), Meguid and Zhong (1997), Deng and Meguid (1999), Zhong and Meguid (1999), Jiang et al (2004), Shtrikman (1962, 1963) and later publications, Budiansky (1965), Eshelby (1957) and later publications, Chen and Lee (2002) as well as Buryachenko (2007). Analytical solutions are either limited to very simple geometries such as elliptical inclusions or require high level of mathematical competence.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic properties of solids with irregularly shaped inclusions

Ping

Chen

2009

Int J Mech Mater Des

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A unit rectangular cell is usually cut out from a medium for investigating fracture mechanism and elastic properties of the medium containing an array of irregularly shaped inclusions. It is desirable to clarify the geometrical parameters controlling the elastic properties of heterogeneous materials because they are usually embedded with randomly distributed particulate. The stress and strain relationship of the rectangular cell is obtained by an ad hoc hybrid-stress finite element method. By matching the boundary condition requirements, the effective elastic properties of composite materials are then calculated, and the effect of shape and arrangement of inclusions on the effective elastic properties is subsequently considered by the application of the ad hoc hybrid-stress finite element method through examining three types of rectangular cell models assuming rectangular arrays of rectangular or diamond inclusions. It is found that the area fraction (the ratio of the inclusion area over the rectangular cell area) is one dominant parameter controlling the effective elastic properties.

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“…In a series of papers, Sabina et al (2002 and references therein) employed Weierstrassian elliptic functions to solve static problems using the MAH for materials of various symmetry and for transversely isotropic phases. Eigenstrain methods (see Nemat-Nasser & Hori 1999) have also been applied in the static context by Jiang et al (2004).…”

Section: Introductionmentioning

confidence: 99%

A new integral equation approach to elastodynamic homogenization

Parnell

Abrahams

2008

Proc. R. Soc. A.

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A new theory of elastodynamic homogenization is proposed, which exploits the integral equation form of Navier's equations and relationships between length scales within composite media. The scheme is introduced by focusing on its leading-order approximation for orthotropic, periodic fibre-reinforced media where fibres have arbitrary cross-sectional shape. The methodology is general but here it is shown for horizontally polarized shear (SH) wave propagation for ease of exposition. The resulting effective properties are shown to possess rich structure in that four terms account separately for the physical detail of the composite (associated with fibre cross-sectional shape, elastic properties, lattice geometry and volume fraction). In particular, the appropriate component of Eshelby's tensor arises naturally in order to deal with the shape of the fibre cross section. Results are plotted for circular fibres and compared with extant methods, including the method of asymptotic homogenization. The leadingorder scheme is shown to be in excellent agreement even for relatively high volume fractions.

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A rigorous analytical method for doubly periodic cylindrical inclusions under longitudinal shear and its application

Cited by 45 publications

References 19 publications

Analysis of fibrous elastic composites with nonuniform imperfect adhesion

Analysis of fibrous elastic composites with nonuniform imperfect adhesion

Effective elastic properties of solids with irregularly shaped inclusions

A new integral equation approach to elastodynamic homogenization

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