Dislocations and internal loading in a semi-infinite elastic medium with surface stresses

Intarit, Pong-in; Senjuntichai, Teerapong; Rajapakse, R. K. N. D.

doi:10.1016/j.engfracmech.2010.04.026

Cited by 31 publications

(6 citation statements)

References 22 publications

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“…The normalized horizontal surface displacement, the normalized vertical surface displacement, and the surface vertical stress generated by the proposed technique are reported in Figures 14, 15 clearly illustrated in Figure 14 and Figure 15. This finding also confirms the conclusion of the various previous researches on that the presence of surface stresses or surface energy renders the material stiffer (Zhao and Rajapakse, 2009, Intarit et al, 2010, Intarit et al, 2011, Zhao and Rajapakse, 2013, Tirapat et al, 2017, Tarntira, 2018. Similarly, as the ratio / s  increases, the vertical stress at the free surface of the bulk reduces over the loading region and becomes larger outside of the loading region.…”

Section: Homogeneous Half-plane Without Surface Stressessupporting

confidence: 90%

SBFE analysis of layered elastic media with consideration of surface energy effect

Chhuon

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This thesis presents an efficient and accurate numerical technique for determining mechanical response of a two-dimensional, infinite, elastic, layered medium under arbitrary surface loading and surface stress effects. Governing equations of a generic bulk layer are formulated from the classical linear elasticity theory via a SBFE technique whereas those of the generic material surface are obtained from a full version of Gurtin-Murdoch surface elasticity theory. The formulation is established sufficiently general allowing both homogenous and functionally graded bulk materials to be treated for each layer. By enforcing the continuity at the interface of the material surface and the bulk, it leads to a system of non-homogenous, linear, ordinary differential equations governing the nodal functions of the layered medium. A general solution of the resulting system of ODEs is then constructed via standard procedures and then used to form a system of linear algebraic equations governing nodal boundary data. To facilitate the treatment of surface loading over a finite region, a SBFE subdomain technique is applied to establish a final system of governing equations for the whole layered medium. To fully investigate the accuracy, convergence, and capability of the proposed method, selected scenarios are solved and obtained numerical results are reported and discussed.

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Section: Homogeneous Half-plane Without Surface Stressessupporting

confidence: 90%

SBFE analysis of layered elastic media with consideration of surface energy effect

Chhuon

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“…Moreover, Kim et al [128] studied the effect of surface elasticity on an interface crack between two dissimilar linearly elastic isotropic homogeneous materials under plane deformation. Intarit et al [129] gave analytical solutions through which the shear and opening dislocations, as well as the corresponding internal vertical and horizontal loading, in an elastic half-plane can be numerically described by using the Gurtin-Murdoch model and the Fourier integral transform method. The last topic in this review is to present a few remarks on contact problems at the nanoscale.…”

Section: Surface Elasticity Theory On Fracture and Contact Mechanicsmentioning

confidence: 99%

Surface effects at the nanoscale based on Gurtin’s theory: a review

Liu

Xia³

2014

Journal of the Mechanical Behavior of Materials

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The fields of nanotechnology and nanoscience are full of opportunities and challenges. The needed modification of classical continuum mechanics to account for the dramatically novel characteristics and phenomena determining the mechanical response of nanomaterials/ structures remains an ambitious goal pursued by mechanics researchers. The theory of surface elasticity proposed by Gurtin and Murdoch has been shown to be an important tool in theoretical nanomechanics. In this paper, we present an overview of recent advances in application of surface elasticity theory at the nanoscale. In particular, we focus on the elastic and plastic deformation, vibration and buckling, fracture and contact behavior of nanoscale solids from one dimension to three dimensions. We hope that this contribution can provide a valuable insight into nanomechanics analysis methods by taking surface effects into account. The results may help to bridge the gap between conventional mechanics and findings from simulation and experiment, in such areas as multifunctional material and micro-electro-mechanical systems.

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“…The Gurtin-Murdoch continuum-based model has been employed to study a variety of problems with the consideration of surface energy effects in the past (e.g. see [4][5][6][7][8][9][10][11][12][13][14]).…”

Section: Introductionmentioning

confidence: 99%

Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

et al. 2018

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A variational formulation of interaction problem is presented in this paper for the analysis of an elastic circular plate under axisymmetric vertical loading resting on an isotropic elastic half-space under the influence of surface energy. The Gurtin-Murdoch surface elasticity theory is adopted to take into account the surface energy effects. The contact surface between the plate and the half-space is assumed to be smooth, and the deflected shape of the plate is represented by a power series of the radial coordinate. The undetermined coefficients in the series are determined through the minimization of the total potential energy functional of the plate-half-space system. The accuracy of the present solution is verified by comparing with existing solutions, and selected numerical results are presented to portray the influence of surface energy effects on interaction between an elastic circular plate and an elastic half-space.

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Dislocations and internal loading in a semi-infinite elastic medium with surface stresses

Cited by 31 publications

References 22 publications

SBFE analysis of layered elastic media with consideration of surface energy effect

SBFE analysis of layered elastic media with consideration of surface energy effect

Surface effects at the nanoscale based on Gurtin’s theory: a review

Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

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