Edge dislocation with surface flexural resistance in micropolar materials

Gharahi, Alireza; Schiavone, Peter

doi:10.1007/s00707-018-2338-5

Cited by 5 publications

(3 citation statements)

References 34 publications

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“…This model has been applied to problems involving holes, inhomogeneities and dislocations in micropolar composites. [10][11][12] In each case we have found meaningful solutions which are corroborated by results in the existing literature. We began an examination of the 'well-posedness' of the fundamental boundary value problems associated with this model in [13] with a discussion of uniqueness of solution.…”

Section: Introductionsupporting

confidence: 87%

“…Specifically, the elastic surface was modeled as a linearly elastic micropolar shell of separate micropolar elasticity allowing the surface to react to bending and micropolar twisting. This model has been applied to problems involving holes, inhomogeneities and dislocations in micropolar composites . In each case we have found meaningful solutions which are corroborated by results in the existing literature.…”

Section: Introductionsupporting

confidence: 81%

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Existence and integral representation of solutions for plane deformations of a micropolar elastic solid with surface elasticity

Gharahi

Schiavone

2020

Z Angew Math Mech

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We consider a linear theory of elastic boundary reinforcement of a micropolar elastic solid subjected to plane-strain deformations. The reinforcement consists of a thin micropolar elastic coating bonded to part of the boundary of the solid. The elastic properties of the coating incorporate both classical and micropolar bending, extension and twisting effects. Interior and exterior mixed boundary problems are formulated and analyzed using the boundary integral equation method. The boundary value problems are reduced to systems of singular integro-differential equations to which Noether-type theorems are shown to apply. We consider also the corresponding boundary value problems based on an alternative lower-order shell model of the reinforcement. Finally, existence and uniqueness results are presented for the corresponding interior and exterior boundary value problems in the appropriate classical function spaces. K E Y W O R D Sexistence of solution, micropolar boundary reinforcement, micropolar surface effects, plane micropolar elasticity, singular integro-differential equations

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Section: Introductionsupporting

confidence: 87%

Section: Introductionsupporting

confidence: 81%

Existence and integral representation of solutions for plane deformations of a micropolar elastic solid with surface elasticity

Gharahi

Schiavone

2020

Z Angew Math Mech

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“…For this purpose, Eremeyev and Lebedev [39] and Zemlyanova and Mogilevskaya [40] rederived the boundary conditions of the Steigmann-Ogden model, using the variational approach. Since then, this model has been successfully employed in a few research areas, including nanocontact mechanics [41][42][43][44][45][46], fracture mechanics [47], dislocation mechanics [48,49], and fibrously reinforced nanocomposites [40,[50][51][52]. Until very recently, the elastic states and effective material properties of particulately reinforced nanocomposites have not been addressed.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions of a spherical nanoinhomogeneity under far-field unidirectional loading based on Steigmann–Ogden surface model

Ban

2020

Mathematics and Mechanics of Solids

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For a solid surface or interface that is subjected to transverse loading, the influence of its flexural resistibility to bending deformation becomes significant. A spherical inhomogeneity or void embedded in an infinite elastic medium under the application of nonhydrostatic loads represents a typical example. In this work, we consider the most fundamental loading of a far-field unidirectional tension. Analytical displacements and stresses are developed by the coupling of a Steigmann–Ogden surface mechanical model, the simple method of Boussinesq displacement potentials, the semi-inverse method of elasticity, and Legendre series representations of spherical harmonics. The problem is then solved by converting the equilibrium equations of displacement into a linear system with respect to the Legendre series coefficients. The developed solutions are general in the sense that they may reduce to their classical or Gurtin–Murdoch counterparts as special cases. Analytical expressions reveal that the derived solution depends on four dimensionless ratios from among surface material parameters, shear moduli ratio, and inhomogeneity or void radius. In particular, instead of depending on both flexural parameters in the moment–curvature relation, one fixed combination is sufficient to represent the surface flexural rigidity. This is in contrast with the influence of the in-plane elastic stiffness, in which both surface Lamé parameters matter. Parametric studies further demonstrate that, for metallic inhomogeneities or voids with radii between 10 nm and 100 nm, the effects of surface flexural rigidity on stress distributions and stress concentrations are significant.

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