On the stress analysis around a nanoinhomogeneity embedded in a half-space with the account of Steigmann–Ogden interface effects

Ban, Youxue; Li, Xiaobao; Li, Ling; Mi, Changwen

doi:10.1016/j.apm.2021.05.015

Cited by 4 publications

(3 citation statements)

References 49 publications

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“…where the function L 2 (x) is defined as before by the second formula (42). The resulting equation can be interpreted as an integral equation for the function G(x) with the kernel which possesses at most a logarithmic singularity at t = x and fixed integrable singularities at x = ±1.…”

Section: A Single Singular Integral Equation For the Function G(x)mentioning

confidence: 99%

“…Eremeyev and Lebedev [18] derived the boundary conditions for the Steigmann-Ogden model and studied the existence and uniqueness of the solutions in certain spaces. The Steigmann-Ogden and the Gurtin-Murdoch theories have been used to study fracture [19][20][21][22][23][24][25][26][27], contact and patch-loading problems [28][29][30][31][32][33][34][35][36][37][38][39], particle and fiber reinforcements [40][41][42][43][44][45][46][47][48][49][50], and other topics [51][52][53][54][55][56][57][58][59][60][61][62][63]. The results are mostly available for the regular shapes of the boundaries of the solids such as straight, circular, or spherical.…”

Section: Introductionmentioning

confidence: 99%

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A problem for a material surface attached to the boundary of an elastic semi-plane

Zemlyanova

2023

Mathematics and Mechanics of Solids

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A problem for a nano-sized material surface attached to the boundary of an elastic isotropic semi-plane is considered. The semi-plane and the material surface are assumed to be in a plane strain state under the action of a normal external tractions applied to the material surface. The material surface is modeled using the Steigmann–Ogden form of surface energy. The problem is solved using integral representations of stresses and displacements. With the help of these representations, the problem can be reduced to either a system of two singular integral equations or a single singular integral equation. Two types of material surface tip conditions are considered: tip conditions with an uncompensated surface prestress (free tip conditions) and tip conditions with a compensated surface prestress term. The numerical solution of the system of singular integral equations is obtained by expanding each unknown function into a series based on the Chebyshev polynomials. Then, the approximations of the unknown functions can be obtained from a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. It is shown that both the surface parameters and the type of tip conditions have significant influence on the behavior of the material system.

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Section: A Single Singular Integral Equation For the Function G(x)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A problem for a material surface attached to the boundary of an elastic semi-plane

Zemlyanova

2023

Mathematics and Mechanics of Solids

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“…Overall, nanoporous materials offer a wide range of advantages and have the potential to revolutionize various fields such as energy, environmental science, biomedicine, and electronics. [1][2][3] Due to the superior properties of nanoporous materials, related research articles have also been developed, including the study of effective modulus 4,5 , elastic response [6][7][8][9] and strength analysis of nanoporous materials 1,2,10,11 .…”

Section: Introductionmentioning

confidence: 99%

Equivalent modulus of nanoporous materials based on Steigman-Ogden surface model

Zheng,

Li,

Zhang

et al. 2023

Preprint

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The work of this paper mainly includes two parts. The first part is to simplify the stress boundary equation of the complex Steigmann-Ogden surface model expressed by the surface gradient operator in spherical coordinates to the stress boundary equation expressed by the spatial gradient operator according to the surface projection tensor. This simplification can directly substitute the complex formula into the fingermark method and directly calculate it into the sizeable mathematical calculation software. In the second part, based on the Mori-Tanaka hole model, the displacement field is decoupled into a hydrostatic and partial displacement field. Based on the homogenization approach, the equivalent elastic modulus of nanoporous materials is solved by satisfying the displacement boundary equation on the boundary of the representative volume element (RVE). The hydrostatic displacement field corresponds to the macroscopic equivalent bulk modulus, while the offset displacement field corresponds to the macroscopic equivalent shear modulus. Finally, this paper conducted auspicious numerical experiments on various surface elastic parameters and explored their control mechanisms. The research in this paper can provide a theoretical basis for designing and manufacturing nanoporous materials.

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On the yield criterion of two-scale porous materials by using Eshelby-type velocity field and Steigmann–Ogden surface model

Zheng

Song²,

2023

Mechanics of Materials

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On the stress analysis around a nanoinhomogeneity embedded in a half-space with the account of Steigmann–Ogden interface effects

Cited by 4 publications

References 49 publications

A problem for a material surface attached to the boundary of an elastic semi-plane

A problem for a material surface attached to the boundary of an elastic semi-plane

Equivalent modulus of nanoporous materials based on Steigman-Ogden surface model

On the yield criterion of two-scale porous materials by using Eshelby-type velocity field and Steigmann–Ogden surface model

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