Local fields and overall transverse properties of unidirectional composite materials with multiple nanofibers and Steigmann–Ogden interfaces

Han, Zhilin; Mogilevskaya, Sofia G.; Schillinger, Dominik

doi:10.1016/j.ijsolstr.2018.05.019

Cited by 53 publications

(33 citation statements)

References 57 publications

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“…The literature on nano-porous materials and nano-particle reinforced composites considering the Steigmann-Ogden surface elasticity model are rather limited (Gharahi and Schiavone, 2018;Han et al, 2018;Zemlyanova and Mogilevskaya, 2018a;Zemlyanova and Mogilevskaya, 2018b), and most of these studies are focused on 2D nano-inhomogeneity problems. Nevertheless, these studies on nano-inhomogeneities have shown that the interface bending resistance can significantly change the local stress distributions as well as the overall properties of nano-composites, and thus it should not be neglected.…”

Section: Introductionmentioning

confidence: 99%

Spherical nano-inhomogeneity with the Steigmann–Ogden interface model under general uniform far-field stress loading

Wang

Yan

Dong

et al. 2020

International Journal of Solids and Structures

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An explicit solution, considering the interface bending resistance as described by the Steigmann-Ogden interface model, is derived for the problem of a spherical nano-inhomogeneity (nanoscale void/inclusion) embedded in an infinite linear-elastic matrix under a general uniform far-field-stress (including tensile and shear stresses). The Papkovich-Neuber (P-N) general solutions, which are expressed in terms of spherical harmonics, are used to derive the analytical solution. A superposition technique is used to overcome the mathematical complexity brought on by the assumed interfacial residual stress in the Steigmann-Ogden interface model. Numerical examples show that the stress field, considering the interface bending resistance as with the Steigmann-Ogden interface model, differs significantly from that considering only the interface stretching resistance as with the Gurtin-Murdoch interface model. In addition to the size-dependency, another interesting phenomenon is observed: some stress components are invariant to interface bending stiffness parameters along a certain circle in the inclusion/matrix. Moreover, a characteristic line for the interface bending stiffness parameters is presented, near which the stress concentration becomes quite severe. Finally, the derived analytical solution with the Steigmann-Ogden interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.6 of 37 pages ellipsoidal, etc.). More complex loads may also be considered, such as far-field bending.The rest of this paper is organized as follows: In Section 2, the governing equations for the 3D nano-inhomogeneity with Steigmann-Ogden interface are briefly stated. In Section 3, the Papkovich-Neuber solutions and spherical harmonics are detailed. Then using the Steigmann-Ogden interface description and the far-field conditions, the explicit analytical solution to the considered nano-inhomogeneity problem is given in Section 4. In Section 5, we discuss the influences of the interface bending on stress distributions within and around the nano-inhomogeneity(nano-void/inclusion), when the far-field tensile/shear loads are applied. In Section 6, we complete this paper with some concluding remarks.

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Section: Introductionmentioning

confidence: 99%

Spherical nano-inhomogeneity with the Steigmann–Ogden interface model under general uniform far-field stress loading

Wang

Yan

Dong

et al. 2020

International Journal of Solids and Structures

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“…As stated above, the latter representations are not valid for the cases involving surface tension and that was the reason why the authors of that work have not been able to solve the problem in more general setting. The two-dimensional solutions for the problem of circular inhomogeneities with the complete Steigmann-Ogden interface model are reported in Zemlyanova and Mogilevskaya (2018b) and Han et al (2018). However, they too were obtained with tedious algebra that, for the case of a single inhomogeneity, could be avoided, if simpler representations of the type used by Christensen and Lo (1979) could be modified to include surface tension.…”

Section: Introductionmentioning

confidence: 99%

Displacements representations for the problems with spherical and circular material surfaces

Mogilevskaya

Кущ

Zemlyanova

2019

The Quarterly Journal of Mechanics and Applied Mathematics

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The displacements representations of the type used by Christensen and Lo (1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of a macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin-Murdoch and Steigmann-Ogden models.

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“…16) we can derive the motion equation in the bulk and the natural boundary condition on S. Using the standard technique of calculus of variations from (2.16), we get the motion equation (2.3) and the dynamic boundary conditions on S and along = ∂S. Indeed, after integration by part, we get…”

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confidence: 99%

Strongly anisotropic surface elasticity and antiplane surface waves

Eremeyev

2019

Phil. Trans. R. Soc. A.

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Within the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic long flexible beams. Physically, the model was motivated by deformations of surface coatings consisting of aligned bar-like elements as in the case of hyperbolic metasurfaces. Using the least action variational principle, we derive the dynamic boundary conditions. The linearized boundary-value problem is also presented. In order to demonstrate the peculiarities of the problem, the dispersion relations for surface anti-plane waves are analysed. We have shown that the bending stiffness changes essentially the dispersion relation and conditions of anti-plane surface wave propagation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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Local fields and overall transverse properties of unidirectional composite materials with multiple nanofibers and Steigmann–Ogden interfaces

Cited by 53 publications

References 57 publications

Spherical nano-inhomogeneity with the Steigmann–Ogden interface model under general uniform far-field stress loading

Spherical nano-inhomogeneity with the Steigmann–Ogden interface model under general uniform far-field stress loading

Displacements representations for the problems with spherical and circular material surfaces

Strongly anisotropic surface elasticity and antiplane surface waves

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