Analysis of displacement and strain fields of a screw dislocation in a nanowire using gradient elasticity theory

Shodja, H.M.; Davoudi, Kamyar M.; Gutkin, M. Yu.

doi:10.1016/j.scriptamat.2008.04.007

Cited by 22 publications

(11 citation statements)

References 35 publications

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“…On the other hand, the classical and gradient solutions are practically coincide far from the dislocation line, when jyj > 5c D . Similar results have been obtained for an infinite homogeneous medium (Gutkin and Aifantis, 1996;Lazar and Maugin, 2006b) and a nanowire (Shodja et al, 2008). The main features of the gradient solution for the strain field are as follows.…”

Section: Displacement and Strain Fieldssupporting

confidence: 76%

“…(2) to consider a screw dislocation in a functionally graded material where the Lamé constants depend on the positions. The special variant of the gradient theory with ' ¼ 0, invented earlier by Altan and Aifantis (1992), has also been applied to cracks (Aifantis, 2003;Ru and Aifantis, 1993a;Aifantis, 1992, 1997;Unger and Aifantis, 2000a,b), dislocations Gutkin and Aifantis, 1996;Gutkin and Aifantis, 1997;Gutkin and Aifantis, 1999c;Shodja et al, 2008), disclinations Gutkin and Aifantis, 1999c), composite materials (Tenek and Aifantis, 2001), line forces (Lazar and Maugin, 2006a) and various cases of line loading on the surface of a half-space (Lazar and Maugin, 2006a;Li et al, 2004). Within this special theory, the stress field remains the same as in the classical elasticity while the displacement and strain fields are modified and the classical singularities are eliminated from them.…”

Section: Introductionmentioning

confidence: 99%

“…In our recent paper (Shodja et al, 2008), we have used the special gradient theory (with ' ¼ 0) to analyze the displacement and strain fields of a screw dislocation in a very long elastically isotropic nanowire with fixed ends. We have shown that the dislocation fields do not contain classical jumps and singularities at the dislocation line and strongly depend on both the dislocation position and nanowire radius, thus demonstrating a non-classical size effect.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

Davoudi

Gutkin

Shodja

2010

International Journal of Solids and Structures

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a b s t r a c tA screw dislocation outside an infinite cylindrical nano-inhomogeneity of circular cross section is considered within the isotropic theory of gradient elasticity. Fields of total displacements, elastic and plastic distortions, elastic strains and stresses are derived and analyzed in detail. In contrast with the case of classical elasticity, the gradient solutions are shown to possess no singularities at the dislocation line. Moreover, all stress components are continuous and smooth at the interface unlike the classical solution. As a result, the image force exerted on the dislocation due to the differences in elastic and gradient constants of the matrix and inhomogeneity, remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size-effect in such a way that the stress level inside the inhomogeneity decreases with its size. The gradient and classical solutions coincide when the distances from the dislocation line and the interface exceed several atomic spacings.

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Section: Displacement and Strain Fieldssupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

Davoudi

Gutkin

Shodja

2010

International Journal of Solids and Structures

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“…doi:10.1016/j.ijsolstr.2009.03.026 inhomogeneities in nano-materials were reviewed by Gutkin (2006). Shodja et al (2008) derived the elastic fields of a dislocated nano-wire using the gradient theory of elasticity.…”

Section: Introductionmentioning

confidence: 99%

Elliptic inhomogeneities and inclusions in anti-plane couple stress elasticity with application to nano-composites

Haftbaradaran

Shodja

2009

International Journal of Solids and Structures

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a b s t r a c tIt is well-known that classical continuum theory has certain deficiencies in predicting material's behavior at the micro-and nanoscales, where the size effect is not negligible. Higher order continuum theories introduce new material constants into the formulation, making the interpretation of the size effect possible. One famous version of these theories is the couple stress theory, invoked to study the anti-plane problems of the elliptic inhomogeneities and inclusions in the present work. The formulation in elliptic coordinates leads to an exact series solution involving Mathieu functions. Subsequently, the elastic fields of a single inhomogeneity in conjunction with the Mori-Tanaka theory is employed to estimate the overall anti-plane shear moduli of composites with uni-directional elliptic cylindrical fibers. The dependence of the anti-plane elastic moduli on several important physical parameters such as size, aspect ratio and rigidity of the fiber, the characteristic length of the constituents, and the orientation of the reinforcements is analyzed. Based on the available data in the literature, certain nano-composite models have been proposed and their overall behavior estimated using the present theory.

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“…Note that in analyzing elastic field induced by dislocations, the conventional nonlocal elasticity model with l 2 ¼ 0 is only capable of removing the stress singularity near the dislocation core region [31], while the gradient elasticity model with l 1 ¼ 0 is only capable of removing the strain singularity near the dislocation core region [34,35]. However, the singularity of the stress and strain fields near the dislocation core can be simultaneously removed if adopting the generalized gradient elasticity model where both l 1 and l 2 are present [36,37]. Now some approaches have been proposed to estimate these gradient coefficients or nonlocal constants via using empirical molecular dynamics and lattice dynamics simulations [38,39].…”

Section: Generalized Gradient Elasticity Beam Modelmentioning

confidence: 99%

Flexural waves of carbon nanotubes based on generalized gradient elasticity

Shen

Song

et al. 2011

Physica Status Solidi (b)

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Using generalized gradient elasticity, this paper studies transverse wave characteristics of carbon nanotubes (CNTs) in a free space and embedded in a surrounding elastic medium. For flexural waves propagating in single-walled CNTs, the phase and group velocities are obtained analytically and they are scale-dependent. For single-walled CNTs surrounded by an elastic medium, waves with frequencies lower than the cut-off frequency cannot travel. For double-walled CNTs, waves of acoustic and optical modes are both present, and the cut-off frequency is dependent on the van der Waals force and the surrounding medium, but independent of the scale parameters. The phase speed of flexural waves is strongly affected by the surrounding medium for very low frequencies, and by gradient coefficients for higher frequencies. Dispersion relations are presented graphically to show the scale effects of wave speed with and without a surrounding elastic medium.

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Analysis of displacement and strain fields of a screw dislocation in a nanowire using gradient elasticity theory

Cited by 22 publications

References 35 publications

A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

A screw dislocation near a circular nano-inhomogeneity in gradient elasticity

Elliptic inhomogeneities and inclusions in anti-plane couple stress elasticity with application to nano-composites

Flexural waves of carbon nanotubes based on generalized gradient elasticity

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