Analytic solution for a circular nano-inhomogeneity with interface stretching and bending resistance in plane strain deformations

Dai, Ming; Gharahi, Alireza; Schiavone, Peter

doi:10.1016/j.apm.2017.10.028

Cited by 42 publications

(32 citation statements)

References 29 publications

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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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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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“…The only works we are aware of are. [34][35][36][37][38][39] Most of these papers focus on analytical solutions for an infinite matrix containing one circular/spherical nano-inhomogeneity (e.g., References 28,31,40,41) and analytical micromechanical methods for overall properties of nano-composites (e.g., References 39,42). These studies show that the interface bending parameters can affect the local stress distributions as well as effective properties of nano-composites, and thus should not be neglected.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to the large number of studies on the mechanics of composites with the Gurtin–Murdoch interface model (e.g., References 18,28‐33 and many others), the literature on nano‐particle reinforced composites with Steigmann–Ogden interfaces is rather limited. The only works we are aware of are 34‐39 . Most of these papers focus on analytical solutions for an infinite matrix containing one circular/spherical nano‐inhomogeneity (e.g., References 28,31,40,41) and analytical micromechanical methods for overall properties of nano‐composites (e.g., References 39,42).…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of complex nano‐structured composites, considering interface stretching and bending effects, using nano‐computational grains

Wang

Yan

Dong

et al. 2020

Numerical Meth Engineering

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Driven by the promising applications of nano-composites, the Steigmann-Ogden (S-O) interface stress model is used together with the classical Elasticity theory to model the effective mechanical properties of nano-composites, considering both interface stretching and bending effects. However, no literature has been reported on analytical or numerical solutions for composites containing multiple three-dimensional nano-inclusions with SO interfaces. In order to overcome this difficulty, a new type of computational grain (CG) is developed with an embedded spherical inclusion and SO matrix/inclusion interface. The stiffness matrix of each CG is computed by a new boundary-type multifield variational principle together with Papkovich-Neuber potentials. By evaluating and assembling stiffness matrices of CGs along with parallel computations, very efficient direct numerical simulations of complex nano-composites with a large number of inclusions in a Representative Volume Element of the nanocomposite are essentially realized. Numerical examples demonstrate the validity and the power of the currently developed CGs. Especially, material models with 10,000 nano-inclusions are simulated in around 50 min on the 16-core workstation. The influence of interface elastic bending parameters and spatial distributions of the nano-inclusions on the overall properties of nano-composites is also investigated in this study.

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“…Composite materials can be viewed as a continuum medium consisting of numerous inhomogeneities, and solutions of such inhomogeneity problems provide a powerful tool in analyzing the effective behavior of composite materials. [10][11][12][13] Coupling among different physical phenomena makes the analysis of the inhomogeneity problem in nonlinear medium considerably more complicated. One such example is thermoelectricity, wherein the electric and thermal transports are nonlinearly coupled.…”

Section: Introductionmentioning

confidence: 99%

Closed‐form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials

Yang²,

et al. 2019

Z Angew Math Mech

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Thermoelectricity is a class of material possessing the ability of interconverting heat and electricity. For the sake of high conversion efficiency, inclusions/fibers are usually introduced into thermoelectric materials. However, the discontinuity of material property and geometry brought by inclusions/fibers might result in severe stress concentration and thus greatly affect the mechanical properties of thermoelectric material in its engineering service. This paper introduces a nonlinear coupled thermal–electrical–mechanical formulation for the plane problem of a circular inhomogeneity embedded in a thermoelectric medium under a combined uniform electric current density and energy flux. A special attention is directed towards the induced thermal stress field which has often neglected in the literature. Using methods based on Cauchy integrals, the complex potentials of the electric field, temperature field and associated stress field are derived explicitly in both the inhomogeneity and the surrounding matrix. The analysis shows that the electrically and thermally induced stress has a linear relationship with the energy flux applied at infinity, but has a nonlinear relationship with the remote electric current density. Numerical simulations are also performed to examine how the inhomogeneity influences the electrically induced thermal stress concentration on the interface. The presented results can be directly used for reliability consideration in design and optimization of thermoelectric composites with circular fibers/inclusions.

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Analytic solution for a circular nano-inhomogeneity with interface stretching and bending resistance in plane strain deformations

Cited by 42 publications

References 29 publications

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

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

Direct numerical simulation of complex nano‐structured composites, considering interface stretching and bending effects, using nano‐computational grains

Closed‐form solutions for a circular inhomogeneity in nonlinearly coupled thermoelectric materials

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