Two approaches to study the effect of surface stresses in an elastic body with a nearly circular nanodefect

Keywords: nearly circular nanodefect, boundary perturbation method (BPM), finite-element method (FEM), stress concentration, surface stress

Abstract

Most of the advanced construction and functional materials are elastically nonuniform, moreover, for many of them, the elongated holes and inclusions are typical, which are similar to a cylinder in form. The strength and physicochemical properties of a material, to a great extent, depend on the peculiarities of the strain-stress state of the near-surface and boundary layers of the materials in the heterogeneous systems. The development of the processes of elastic deformation and fracture in these areas, to a large extent, determines the mechanical behavior of a material in general and arouses much interest. The authors study the influence of interfacial stresses on the strain-stress state of elastic bimaterial with smooth waveform interface; consider the 2-D solid mechanics problem of an elastic body with nanoscale boundary surface texture, which appears between the nearly circular inclusion and the matrix. It is expected that a body is situated within a uniform stress field. To solve the problem, the authors used the simplified Gurtin–Murdoch’s surface/interface elasticity model, where the interfacial boundary is the negligibly thin layer exactly bordered on the bulk phases. It is acknowledged that there are no displacement discontinuities on the interfacial boundary, and the stress jump is determined by the effect of surface/interfacial stress according to the generalized Laplace–Young law. Using the boundary perturbation method, the problem solution for each approximation is limited to a singular integrodifferential equation against the unknown surface/interfacial stress. The paper gives the numerical results for the problem to a first approximation. As a result, the authors carry out the comparative analysis of the strain-stress state using the finite-element method and analytical boundary perturbation method.

Author Biographies

Aleksandra B. Vakaeva, St. Petersburg State University, St. Petersburg (Russia)

PhD (Physics and Mathematics), senior lecturer

Gleb M. Shuvalov, St. Petersburg State University, St. Petersburg (Russia)

assistant

Sergey A. Kostyrko, St. Petersburg State University, St. Petersburg (Russia)

PhD (Physics and Mathematics), Associate Professor

Olga S. Sedova, St. Petersburg State University, St. Petersburg (Russia)

PhD (Physics and Mathematics), senior lecturer

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Published
2020-03-28
Section
Technical Sciences