Wrinkling Analysis of Double Nanofilms Embedded in Compliant Substrates Based on Nonlocal Elasticity Theory

Abstract

In this paper, an analytical approach for wrinkling analysis of double nanofilms embedded in compliant substrates is presented. The governing differential equations for wrinkling of double nanofilms are derived based on Eringen’s nonlocal elasticity theory and the classical plate theory (CLPT). Substrates are regarded as elastic bodies of finite thickness and the normal pressure of substrates on the films is assumed to be linear with the lateral deformation of the films. Solutions for critical wrinkling load and wave number are computed in terms of the nonlocal parameter, the elastic properties and thickness of double nanofilms, the elastic properties and thickness of the substrates, and wrinkle modes. The parametric study shows that the dimensionless critical wave number and the dimensionless critical load decrease gradually with the increase of the nonlocal parameter. Four typical wrinkling states are studied: in-phase wrinkling, out-of-phase wrinkling, single-film wrinkling and asymmetric wrinkling. In-phase wrinkling has the highest chance to occur among four wrinkle modes. In addition, the results show that the dimensionless critical load and wave number are much smaller when the films become much stiffer and thinner than the substrates.