Electro-elastic fields around two arbitrarily-shaped holes in a finite electrostrictive solid

Dai, Ming; Meng, Li-Cheng; Huang, Cheng Liang; Gao, Cun‐Fa

doi:10.1016/j.apm.2015.12.001

Cited by 16 publications

(3 citation statements)

References 32 publications

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“…We note that the domain of definition of the complex functions φ ( z ) and ψ ( z ) can be treated as the intersection of two specific regions, one of which is the infinite region outside the curve L while the other is a complete square region (without any hole) bounded by the edge ABCD of the RUC. Consequently, a (truncated) series representation of φ ( z ) can be given by [15]…”

Section: Solution For the Complex Potentialsmentioning

confidence: 99%

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Stress field in a porous material containing periodic arbitrarily-shaped holes with surface tension

Yang

Dai

Gao

2016

Mathematics and Mechanics of Solids

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In the mechanical analysis of a structure/composite with periodic holes/inhomogeneities based on analytic techniques, the holes/inhomogeneities are usually assumed to be circular. In this paper, we develop an efficient method (based on complex variable techniques) to calculate the surface tension-induced stress field in a porous material containing a periodic array of unidirectional holes of arbitrary shape. In this method, we use conformal mapping and Faber series techniques to address a finite representative unit cell (RUC) consisting of a single arbitrarily-shaped hole with a constant surface tension imposed on the hole’s boundary and periodic deformations imposed on the edge of the RUC. Several numerical examples are presented to verify the accuracy of our method and to study the influence of the shape and volume fraction of the periodic holes on the stress concentration in the structure. We show that the maximum hoop stress around periodic holes of some shapes (such as triangle, pentagon or hexagon) may appear exactly at the point(s) of maximum curvature when the hole volume fraction exceeds a certain value. Moreover, when the hole volume fraction falls below about 7%, it is found that the surface tension-induced stress concentration around periodic holes can be treated approximately as that around a single hole with the same hole shape and size in an infinite plane.

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Section: Solution For the Complex Potentialsmentioning

confidence: 99%

“…and denoting the complex functions u(z) and c(z) in equations (13) and (15) with known coefficients X i and Y i (i = 0.4) by u i (z) and c i (z) (i = 0.4), respectively, we can describe the actual stress components in the matrix as…”

Section: Solution For the Complex Potentialsmentioning

confidence: 99%

Stress field in a porous material containing periodic arbitrarily-shaped holes with surface tension

Yang

Dai

Gao

2016

Mathematics and Mechanics of Solids

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“…In numerical investigations concerning the deformation of finite elastic bodies (see, for example, Dai et al [ 11 ]), it is preferable to use truncated Faber series. Specifically, the unknown complex potential of an arbitrarily shaped elastic body (occupying a simply connected region S 1 ) is usually described (approximately) by a truncated Faber series as…”

Section: Replacement Of the Faber Series By Taylor Seriesmentioning

confidence: 99%

Clarification of Faber series and related applications to complex variable methods in two-dimensional elasticity

Dai

Schiavone

2023

Mathematics and Mechanics of Solids

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Faber series are used extensively in the application of complex variable methods to two-dimensional elasticity theory, for example, in the mechanical analysis of composite materials where Faber series representations of complex potentials lead to convenient expressions for the corresponding displacement and stress distributions. In many cases, the use of the Faber series is combined with conformal mapping techniques which “transfer” a boundary value problem defined in the elastic body (physical plane) to a simpler problem posed in an imaginary plane characterized by the conformal mapping. In several instances in the literature, however, little attention has been paid to the domain of definition of the Faber series in the imaginary plane leading often to misunderstandings and erroneous conclusions regarding the concept and feasibility of the use of the Faber series. In this paper, we present a thorough and rigorous examination of the representation of the Faber series in both the physical (occupied by the material) and imaginary (defined by the conformal mapping) plane. In addition, we show that replacing a truncated Faber series by a truncated Taylor series does not induce any additional errors in the numerical analysis of the corresponding boundary value problem. We anticipate that the discussion in this paper will help clarify any existing misinterpretations regarding the application of the Faber series and help further extend their use to a range of problems in composite mechanics.

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Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

Dai

Schiavone

Gao

2016

Z. Angew. Math. Phys.

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Electro-elastic fields around two arbitrarily-shaped holes in a finite electrostrictive solid

Cited by 16 publications

References 32 publications

Stress field in a porous material containing periodic arbitrarily-shaped holes with surface tension

Stress field in a porous material containing periodic arbitrarily-shaped holes with surface tension

Clarification of Faber series and related applications to complex variable methods in two-dimensional elasticity

Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

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