Multilayered Elastic Medium under Axisymmetric Loading and Surface Energy

Abstract

This paper presents a solution scheme for analysis of a multilayered elastic medium under axisymmetric loading and surface energy effects by adopting Gurtin-Murdoch surface elasticity theory. Love’s strain function and Hankel integral transform are employed to derive the general solutions, and the obtained solutions are employed in the determination of the stiffness matrix for each layer. The global stiffness equation of a multi-layered system is assembled by considering the continuity of traction and displacements at each layer interface. The numerical solutions to the global equation yield displacements and stresses at the interfaces of the layered medium under axisymmetric loading. The accuracy of the proposed solution scheme is verified by comparing with existing solutions. Selected numerical results are presented to demonstrate a significant influence of surface energy on elastic fields of a multilayered elastic medium under axisymmetric loading.

Elastic solution of surface loaded layer with couple and surface stress effects

“…Within the context of surface mechanics, applications of such theory to study the near-surface responses have also been well recognized; for instance, problems related to half plane, half space, and layered media under surface loads (e.g. 7,8,[51][52][53][54] ) and surface contacts [55][56][57][58][59][60][61][62] . Results from existing studies have confirmed the significant role of both residual surface tension and surface elasticity on the predicted responses and the size dependent characteristics as the relevant external length scales become comparable to the intrinsic length scale of the material surface.…”

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

“…The key motivation of integrating the influence of surface stresses in the mathematical model relies upon the fact that materials at a nano-scale exhibit very high surface to volume ratio resulting in excess surface free energy caused by the exclusive surface's atom arrangement and, as a direct consequence, rendering their response strongly size-dependent especially when the internal length scale of materials and the external characteristic length of the problems are comparable (Dingreville et al, 2005). Within the context of surface and contact mechanics, recent applications of G-M surface elasticity has also been recognized (Rungamornrat et al, 2016, Tarntira, 2018, Pinyochotiwong et al, 2013, Intarit et al, 2018. Nevertheless, most of existing studies found in the literature are quite limited in two folds, one associated with boundary value problems formulated in rather simple settings and the other corresponding to the solution techniques employed.…”

“…Unlike the body treatment in a classical sense, the body, here, can be separated into the surface and the bulk in which the former is mathematically treated as the zerothickness material layer perfectly adhered to the bulk with its behavior governed by constitutive laws exhibiting different properties from the bulk. With the integration of the surface effect through such the material layer, an intrinsic length scale of materials is automatically introduced, and the resulting mathematical model can now capture the size-dependent behavior (Pinyochotiwong et al, 2013, Intarit et al, 2018, Tirapat and Senjuntichai, 2018, Tirapat et al, 2017, Tarntira, 2018.…”

“…The most recent research on the investigation of mechanical responses of threedimensional elastic layered media under axisymmetric surface loading with the consideration of surface energy effects was conducted by Tarntira (2018). In this work, the medium was modeled as multiple homogeneous layers of constant thickness perfectly bonded at the interface.…”

“…While the work of Tarntira (2018) has the capability to treat a layered medium consisting of arbitrary number of layers, the solution procedure employed raises certain important issues related to the computational efficiency when dealing with large scale problems and the practical application to treat functionally graded material layers. More powerful solution techniques are still required to further upgrade the modeling capability of simulating multi-layered media with a set of general data.…”