Stiffness Contrast and Separation Influence Wrinkling of Adjacent Layers in a Homogeneous Matrix

Abstract

In this paper, we study the wrinkling instability of two layers embedded in a homogeneous matrix of infinite size. Using a linear stability analysis, we characterize the wrinkling of the two layers as a function of the layer spacing and the shear moduli ratio between the two materials. When the layers are stiffer than the surrounding matrix, stiffness contrast largely determines the stability behavior of the system. When the layers are softer than the surrounding matrix, stiffness contrast and layer spacing interact to determine critical threshold strain and wavelength, and result in striking discontinuities in wavelength between regimes. When the layers are close to each other, the system has a strong preference for the symmetric wrinkling mode, but as the distance between the two layers increases, the anti-symmetric mode may emerge.