Complex potential theory for the plane elasticity problem of decagonal quasicrystals and its application

Li, Lianhe

doi:10.1016/j.amc.2013.03.075

Cited by 8 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The certainty of the complex potential function is discussed by means of Equations ( 9)-( 12) in reference [39], and the expression is as follows:…”

Section: Basic Equationmentioning

confidence: 99%

“…Using the complex method, Wang and Zhong [38] studied the interaction of a linear dislocation with a semiinfinite crack in decagonal quasicrystals, and obtained stress intensity factors, energy release rate, and expressions of the Peach-Koehler force acting on the linear dislocation. Li [39] developed the Muskhelishvili method of two-dimensional decagonal quasicrystal plane elasticity theory. Based on the complex representation of stress and displacement, the method of determining the complex potential function is discussed and applied to the study of elliptical holes, and the corresponding analytical solution is obtained.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

2023

Crystals

View full text Add to dashboard Cite

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method of two-dimensional QCs is developed to solve the plane elasticity problem of two-dimensional decagonal QCs containing complex defects. The analytical solutions for the stress field and the stress intensity factors near the crack tip are expressed by using a conformal mapping technique and complex potential theory. Some special cases of the results are also obtained, such as the T-type crack, cross crack, and Griffith crack. The effects of geometrical parameters of crack configuration on the stress intensity factors are presented graphically.

show abstract

“…The certainty of the complex potential function is discussed by means of Equations ( 9)-( 12) in reference [39], and the expression is as follows:…”

Section: Basic Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

2023

Crystals

View full text Add to dashboard Cite

show abstract

“…Wang and Zhong studied the interaction between a semi-infinite crack and a line dislocation in a decagonal quasicrystal solid using the complex variable method [12]. Li constructed the complex potential theory of two-dimensional decagonal quasicrystals and further developed Muskhelishvili's complex variable method [13]. Fan et al studied the interface crack problem of two-dimensional decagonal quasicrystal bi-material using the propagation displacement discontinuity method [14].…”

Section: Introductionmentioning

confidence: 99%

A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials

Zhang,

et al. 2024

Crystals

View full text Add to dashboard Cite

Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension–shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex representation of stress and displacement is given. Using the mixed boundary conditions, the closed-form expressions for the stresses and the displacement jumps in the phonon field and phason field on the material interface are obtained. The results show that the stress intensity factor at the crack tip is zero for the phason field. The variation in the stress intensity factor and the length of the contact zone in the phonon field is given, and the result is consistent with the properties of the crystal. The design of safe engineering structures and the formulation of reasonable quality acceptance standards may benefit from the theoretical research carried out here.

show abstract

“…QCs have been found to be linear-elastic and brittle at ordinary temperature. Therefore, QCs are sensitive to dislocations (Li and Fan, 1999; Liu et al, 2005), holes (Guo and Lu, 2011; Li, 2013), and cracks (Guo et al, 2013; Li, 2014). These defect problems may limit their application and popularity, so it is desirable to further study these problems of QCs.…”

Section: Introductionmentioning

confidence: 99%

Electroelastic Green’s function of one-dimensional piezoelectric quasicrystals subjected to multi-physics loads

Zhang

et al. 2016

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

Green’s functions of infinite and semi-infinite plane problems of one-dimensional quasicrystals with piezoelectric effect are obtained in a closed form by Stroh formalism. Some numerical examples under different loading conditions, such as line forces, line dislocations, and a line charge, are given to explain the mechanical and electric behaviors of the quasicrystals. Various elastic–electric constants of quasicrystals are analyzed and the coupling effects between the phonon and phason fields are studied. The presented solutions will be useful for many boundary value problems of one-dimensional quasicrystals with piezoelectric effect. Moreover, the numerical results can be used to verify the accuracy of the solutions by some numerical methods, such as the finite element and boundary element methods. Furthermore, the Stroh formalism can be generalized to the researches on more complex problems of quasicrystals.

show abstract

Complex potential theory for the plane elasticity problem of decagonal quasicrystals and its application

Cited by 8 publications

References 20 publications

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials

Electroelastic Green’s function of one-dimensional piezoelectric quasicrystals subjected to multi-physics loads

Contact Info

Product

Resources

About