A Straight Dislocation in One-Dimensional Hexagonal Quasicrystals

Li, Xian-Fang; Tang, Fan

doi:10.1002/(sici)1521-3951(199903)212:1<19::aid-pssb19>3.0.co;2-o

Cited by 39 publications

(23 citation statements)

References 14 publications

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“…If we omit the dynamical terms in eq. ( 62), then the obtained force is in accordance with the Peach-Koehler force that has been derived by Li and Fan [37]. In addition, eq.…”

Section: Balance Law Of Pseudomomentum-peach-koehler Forcesupporting

confidence: 82%

Generalized dynamics of moving dislocations in quasicrystals

Agiasofitou

Lazar

Kirchner

2010

J. Phys.: Condens. Matter

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A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation density tensors and introducing the dislocation current tensors for the phonon and phason fields, including the Bianchi identities. Next, we give the equations of motion for the incompatible elastodynamics as well as for the incompatible elasto-hydrodynamics of quasicrystals. We continue with the derivation of the balance law of pseudomomentum thereby obtaining the generalized forms of the Eshelby stress tensor, the pseudomomentum vector, the dynamical Peach-Koehler force density and the Cherepanov force density for quasicrystals. The form of the dynamical Peach-Koehler force for a straight dislocation is obtained as well. Moreover, we deduce the balance law of energy that gives rise to the generalized forms of the field intensity vector and the elastic power density of quasicrystals. The above balance laws are produced for both models. The differences between the two models and their consequences are revealed. *

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“…If we omit the dynamical terms in eq. ( 62), then the obtained force is in accordance with the Peach-Koehler force that has been derived by Li and Fan [37]. In addition, eq.…”

Section: Balance Law Of Pseudomomentum-peach-koehler Forcesupporting

confidence: 82%

Generalized dynamics of moving dislocations in quasicrystals

Agiasofitou

Lazar

Kirchner

2010

J. Phys.: Condens. Matter

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“…The J -integral given by Eq. ( 148) represents the Peach-Koehler force for straight dislocations in arbitrary quasicrystals in statics and it is in agreement with Li and Fan [1999]. The dynamical Peach-Koehler force for straight dislocations in arbitrary quasicrystals has been derived by Agiasofitou et al [2010].…”

Section: Two-dimensional Quasicrystals: Decagonal Quasicrystalsmentioning

confidence: 55%

“…Shi [2005Shi [ , 2007 was the first to study conservation laws and the corresponding path-independent integrals for quasicrystals. The static Peach-Koehler force for straight dislocations in one-dimensional hexagonal quasicrystals was first derived by Li and Fan [1999]. In the framework of fracture mechanics, Fan and Mai [2004] (see also [Fan, 2011]) derived a "generalized Eshelby integral", which has the physical meaning of a J 1 -integral, in terms of a generalized Eshelby stress tensor for quasicrystals.…”

Section: ]mentioning

confidence: 99%

Eshelbian mechanics of novel materials: Quasicrystals

Lazar

Agiasofitou

2016

J. Micromech. Mol. Phys.

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In this work, the so-called Eshelbian or configurational mechanics of quasicrystals is presented. Quasicrystals are considered as a prototype of novel materials. Material balance laws for quasicrystalline materials with dislocations are derived in the framework of generalized incompatible elasticity theory of quasicrystals. Translations, scaling transformations as well as rotations are examined; the latter presents particular interest due to the quasicrystalline structure. This derivation provides important quantities of the Eshelbian mechanics, as the Eshelby stress tensor, the scaling flux vector, the angular momentum tensor, the configurational forces (Peach-Koehler force, Cherepanov force, inhomogeneity force or Eshelby force), the configurational work and the configurational vector moments for dislocations in quasicrystals. The corresponding J-, M -, and L-integrals for dislocation loops and straight dislocations in quasicrystals are derived and discussed. Moreover, the explicit formulas of the J-, M -, and L-integrals for parallel screw dislocations in one-dimensional hexagonal quasicrystals are obtained. Through this derivation, the physical interpretation of the J-, M -, and L-integrals for dislocations in quasicrystals is revealed and their connection to the Peach-Koehler force, the interaction energy and the rotational vector moment (torque) of dislocations in quasicrystals is established.

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“…The properties of quasicrystals are affected by defects such as dislocations, cracks, holes, and inclusions. Li and Fan [9] considered a straight dislocation in one-dimensional (1D) hexagonal quasicrystals. Fan et al [10] studied the problem of a moving screw dislocation in 1D hexagonal quasicrystals.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

2021

Appl. Math. Mech.-Engl. Ed.

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The explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

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A Straight Dislocation in One-Dimensional Hexagonal Quasicrystals

Cited by 39 publications

References 14 publications

Generalized dynamics of moving dislocations in quasicrystals

Generalized dynamics of moving dislocations in quasicrystals

Eshelbian mechanics of novel materials: Quasicrystals

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

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