A new type of boundary layers, a representative model, and surface wrinkling in inhomogeneous plates

TL;DR

This paper introduces a new boundary layer type specific to inhomogeneous plates, proposes a representative model for complex layered structures, and identifies surface wrinkling phenomena unique to inhomogeneous materials, highlighting potential adverse effects.

Contribution

It presents the discovery of a novel boundary layer type, a new concept of representative plates, and the observation of surface wrinkling in inhomogeneous plates, which are absent in homogeneous ones.

Findings

New boundary layer type at inhomogeneous plate surfaces

Representative plate model for complex layered structures

Surface wrinkling phenomenon in inhomogeneous plates

Abstract

We find a new type of boundary layers that occur at the top and bottom surfaces of an inhomogeneous plate. The boundary layers of this type never occur in homogeneous plates or plates made of layers of homogeneous materials. The thickness of such a boundary layer is usually less than that of a one single fiber of the plate. Moreover, we introduce a new notion of representative plate as a plate whose stress-strain state in some parts is similar to the stress-strain state in the original plate. In addition, every part of the original plate has a corresponding part in the representative plate. We demonstrate that a three-layered plate can be representative of a plate formed of an arbitrary number of layers. We also demonstrate a wrinkling phenomenon that happens on the top and bottom surfaces of inhomogeneous plates. This effect does not occur in homogeneous plates or plates made of layers of homogeneous materials. Such wrinkling can become a significant adverse effect, and thus should be given utmost attention.