Surface and interfacial anti-plane waves in micropolar solids with surface energy

Chaki, Mriganka Shekhar; Eremeyev, Victor A.; Singh, Abhishek Kumar

doi:10.1177/1081286520965646

Cited by 9 publications

(8 citation statements)

References 54 publications

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“…It is worth mentioning that the above contact laws establish a generalization to the case of strain gradient elasticity of the so-called coherent or Gurtin-Murdoch's interface model, according to which the traction vector suffers a jump discontinuity, satisfying a two-dimensional Laplace-Young equation. This particular model has been first developed for continuum theories with surface effects by the early work of Gurtin & Murdoch [52] and applied to surface and interfacial wave propagation by [53][54][55]. Indeed, the term ℎL αβ u , αβ 0 represents the divergence of a surface stress tensor defined on the plane of the interface, equivalent to the one introduced in [52].…”

Section: (E) the Interface Conditionsmentioning

confidence: 99%

Hard interfaces with microstructure: the cases of strain gradient elasticity and micropolar elasticity

Serpilli,

Rizzoni,

Lebon

2024

Phil. Trans. R. Soc. A.

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As the size of a layered structure scales down, the adhesive layer thickness correspondingly decreases from macro- to micro-scale. The influence of the material microstructure of the adhesive becomes more pronounced, and possible size effect phenomena can appear. This paper describes the mechanical behaviour of composites made of two solids, bonded together by a thin layer, in the framework of strain gradient and micropolar elasticity. The adhesive layer is assumed to have the same stiffness properties as the adherents. By means of the asymptotic methods, the contact laws are derived at order 0 and order 1. These conditions represent a formal generalization of the hard elastic interface conditions. A simple benchmark equilibrium problem (a three-layer composite micro-bar subjected to an axial load) is developed to numerically assess the asymptotic model. Size effects and non-local phenomena, owing to high strain concentrations at the edges, are highlighted. The example proves the efficiency of the proposed approach in designing micro-scale-layered devices. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

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Section: (E) the Interface Conditionsmentioning

confidence: 99%

Hard interfaces with microstructure: the cases of strain gradient elasticity and micropolar elasticity

Serpilli,

Rizzoni,

Lebon

2024

Phil. Trans. R. Soc. A.

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“…A n e β n kx 2 e i(kx 1 −ωt) , ψ = Be kx 2 e i(kx 1 −ωt) , φ = e −kx 2 e i(kx 1 −ωt) , (30) where β n > 0 are the attenuation coefficients.…”

Section: Bleustein-gulyaev Wavementioning

confidence: 99%

“…Substituting solution (30) into boundary conditions ( 28) and ( 29), one will obtain the following system:…”

Section: Fundingmentioning

confidence: 99%

Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

Solyaev

2023

Mathematics and Mechanics of Solids

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In this paper, we present a variant of the second gradient continuum model that allows description of the spatial dispersion effects of high-frequency waves in anisotropic crystals. The considered model takes into account the strain and inertia gradient effects and the classical electro-mechanical coupling. The simplified constitutive equations of the model contain seven and four length scale parameters for piezoelectric hexagonal crystals and elastic cubic crystals, respectively. It is shown that all except one length scale parameter can be identified based on the fitting of the continuum model to the lattice dynamics calculations for the dispersion relations of the bulk acoustic phonons. Examples of the identification are presented for hexagonal piezoelectric ZnO and AlN and for cubic diamond and Si crystals. Using a calibrated model, we then obtain the dispersion relations for the high-frequency Bleustein–Gulyaev wave in piezoelectric crystals and for the shear horizontal surface wave in elastic crystals. The last one is predicted by the gradient models only for the high frequencies, while at low frequencies this wave degenerates to the bulk shear wave. Examples of calculations are also provided for the Rayleigh wave propagating through the homogeneous piezoelectric half-space and layered ZnO(AlN)/diamond/Si structures. It is shown that this kind of surface wave can be used to identify the last unknown length scale parameter of the model.

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“…To this end, one can transform δE and δA using Eulerian coordinates. Changing coordinates X → x in (49) and using (19) and (21), one has…”

Section: Lagrange Variational Principlementioning

confidence: 99%

“…The boundary conditions of the normal gradient of mass density are introduced first on logical grounds and only subsequently they are physically interpreted. More recent discussion of novel boundary conditions that can be introduced in second continuum theories can be found in [21,[41][42][43]47,50,109]. In particular, the interrelations between Toupin-Mindlin strain gradient elasticity with the surface elasticity by Gurtin-Murdoch were analysed in [50], whereas similar comparison of surface phenomena within the lattice dynamics was provided in [51,117].…”

Section: Introductionmentioning

confidence: 99%

On nonlinear dilatational strain gradient elasticity

Eremeyev

Cazzani

Dell’Isola

2021

Continuum Mech. Thermodyn.

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We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the only second gradient effects are due to the inhomogeneous dilatation state of the considered deformable body. The dilatational second gradient continua are strictly related to other generalized models with scalar (one-dimensional) microstructure as those considered in poroelasticity. They could be also regarded to be the result of a kind of “solidification” of the strain gradient fluids known as Korteweg or Cahn–Hilliard fluids. Using the variational approach we derive, for dilatational second gradient continua the Euler–Lagrange equilibrium conditions in both Lagrangian and Eulerian descriptions. In particular, we show that the considered continua can support contact forces concentrated on edges but also on surface curves in the faces of piecewise orientable contact surfaces. The conditions characterizing the possible externally applicable double forces and curve forces are found and examined in detail. As a result of linearization the case of small deformations is also presented. The peculiarities of the model is illustrated through axial deformations of a thick-walled elastic tube and the propagation of dilatational waves.

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Surface and interfacial anti-plane waves in micropolar solids with surface energy

Cited by 9 publications

References 54 publications

Hard interfaces with microstructure: the cases of strain gradient elasticity and micropolar elasticity

Hard interfaces with microstructure: the cases of strain gradient elasticity and micropolar elasticity

Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

On nonlinear dilatational strain gradient elasticity

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