Surface effects in anti-plane deformations of a micropolar elastic solid: integral equation methods

Sigaeva, Taisiya; Schiavone, Peter

doi:10.1007/s00161-014-0404-3

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…[5,15,21,22] In our case, however, the BIEM, is complicated by the fact that the incorporation of surface elasticity leads to a set of highly non-standard boundary conditions that require special attention. A similar situation was encountered and addressed for classical elastic materials in [24,25] and for antiplane deformations of a micropolar surface-bulk model in [26]. Here, we further extend the BIEM to accommodate the higher order theory involving plane deformations of micropolar bulk-surface models.…”

Section: Introductionmentioning

confidence: 61%

“…In this section we focus on the term * ( ) −1 ( ) ∫ Γ ( , ) ( ) ( ) , which appears in both interior and exterior problems. Before analyzing the foregoing integral, we remind ourselves that the first integral on the right-hand side of both Equations (22) and (26) has been investigated by Iesan [15] and Schiavone [22] :…”

Section: Singular Integro-differential Equation In the Standard Formmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 61%

Section: Singular Integro-differential Equation In the Standard Formmentioning

confidence: 99%

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

Gharahi

Schiavone

2020

Z Angew Math Mech

Self Cite

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“…Wheras, in the micropolar plate case, an additional set of constitutive equations relates the couple stresses and the rotation gradients with three additional material constants. We already presented these in terms of the rotational kinematic components in equation (5). To obtain the governing equations of the micropolar plate with surface elastic effects, we incorporate the equations (12)(13)(14)(15) into the sixcomponent balance equations (6)(7)(8)(9).…”

Section: Equilibrium Equations Of the Micropolar Thin Platementioning

confidence: 99%

“…Different paradigms for extending the continuum theories are developed in response to the two different sources of size-dependence, namely: surface effects, and internal micro/nano-structure effects. However, a combined approach designed to extend the continuum models to incorporate the effects of both surfaces and internal micro/nano structures at the micro/nano scales, is seldom found in the literature [4,5].…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity

Gharahi

2024

J Elast

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We generalize a recent theory of bending of thin micropolar plates by incorporating surface effects through the modeling of plate surfaces as adjacent two-dimensional micropolar elastic bodies. By incorporating both elastic surface effects and the micropolar elastic behavior of the plate, the proposed model is capable of taking into account the contribution of high surface-to-volume ratios as well as the influence of microstructural mechanics at micro/nano scales. We determine the fundamental solution of the resulting system of equations and establish uniqueness results for the corresponding Dirichlet and Neumann boundary value problems. Moreover, we provide a numerical example to demonstrate the efficiency of the model in representing the size-dependence arising from various factors that incorporate characteristic lengths. Furthermore, we showcase the sensitivity of the results to different types of characteristic lengths present in the model.

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Uniqueness of solution for plane deformations of a micropolar elastic solid with surface effects

Gharahi

Schiavone

2019

Continuum Mech. Thermodyn.

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Surface effects in anti-plane deformations of a micropolar elastic solid: integral equation methods

Cited by 6 publications

References 15 publications

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

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

Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity

Uniqueness of solution for plane deformations of a micropolar elastic solid with surface effects

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