Surface elasticity and residual stress effect on the elastic field of a nanoscale elastic layer

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

doi:10.12989/imm.2011.4.2.085

Cited by 16 publications

(9 citation statements)

References 16 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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“…Equation (4) can be viewed as the outof-plane contribution of the preexisting surface tension in the deformed configuration whereas the surface gradient of the displacement / acts as the out-of-plane component of the unit vector tangent to the surface in the deformed state. This term has been ignored in several previous studies even though the contribution of could be significant even in the case of small deformations (e.g., see [17,18,20]). The general solutions for the stresses and displacements in the bulk material under axisymmetric deformations can be expressed by using Love's strain potential and Hankel integral transform as [32]…”

Section: Governing Equations and General Solutionsmentioning

confidence: 99%

“…Wang et al [16] showed that the out-of-plane terms of the surface displacement gradient could be significant even in the case of small deformations particularly for curved and rotated surfaces. The complete version of Gurtin-Murdoch model, with consideration of the out-of-plane term, has later been employed to examine various continuum mechanics problems, for example, problems related to an internally loaded elastic layer under plane-strain condition [17] and axisymmetric loading [18], respectively; contact problem [19]; nanoindentation [20,21]; nanobeams [22]; nanoplate [23]; and nanosized cracks [24,25]. In addition, the influence of surface energy is also significant in problems related to soft elastic solids [26].…”

Section: Introductionmentioning

confidence: 99%

Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading

Tirapat

Senjuntichai

Rungamornrat

2017

Advances in Materials Science and Engineering

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This paper presents the analysis of a layered elastic half space under the action of axisymmetric surface loading and the influence of the surface energy effects. The boundary value problems for the bulk and the surface are formulated based on classical linear elasticity and a complete Gurtin-Murdoch constitutive relation. An analytical technique using Love’s representation and the Hankel integral transform is employed to derive an integral-form solution for both displacement and stress fields. An efficient numerical quadrature is then applied to accurately evaluate all involved integrals. Selected numerical results are presented to portray the influence of various parameters on elastic fields. Numerical results indicate that the surface stress displays a significant influence on both displacement and stress fields. It is also found that the layered half space becomes stiffer with the presence of surface stresses. In addition, unlike the classical elasticity solution, size-dependent behavior of elastic fields is noted. The present analytical solutions provide fundamental understanding of the influence of surface energy on layered elastic materials. It can also be used as a benchmark solution for the development of numerical techniques such as FEM and BEM, for analysis of more complex problems involving a layered medium under the influence of surface energy effects.

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“…Therefore, the Gurtin-Murdoch (GM) surface elasticity theory has been adopted to elucidate many sizedependent phenomena at nanoscale. For instance, ultra-thin elastic films ( [7][8][9][10]), nano-inclusion ( [11,12]), nanoscale inhomogeneities ( [13][14][15]), and nanoscale elastic layers ( [16,17]). This should additionally confirm the benefit of employing such alternative continuum-based model to save the computational resources with an acceptable level of accuracy gained.…”

Section: Introductionmentioning

confidence: 99%

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

Attia

Mahmoud

2015

International Journal of Mechanical Sciences

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Surface elasticity and residual stress effect on the elastic field of a nanoscale elastic layer

Cited by 16 publications

References 16 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

Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

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