Buckling of stretched disks—With comparisons and extensions to auxetics

Abstract

In this paper, we investigate the instability behavior of thin elastic circular disks subjected to two concentrated edge loads arranged along a diameter. Despite the determination of critical load intensities for disks, made of conventional, linear elastic material, under some specific boundary conditions has been published in the past, we show some new and quite interesting findings. Particularly new are the investigations of tensile buckling of completely free disks as well as the post-buckling behavior of such disks under tension and compression, respectively. Comparisons with already existing results are presented, too. As far as the buckling load is concerned, all results are expressed in terms of a non-dimensional buckling factor. It is well known that the use of auxetic materials provides some potential for improving the behavior of lightweight structures. This fact has motivated us to consider, in which way the variation of the Poisson's ratio ν influences the stability behavior of the disks both under compression and under tension not just for the so far not investigated completely free stretched disks but also for the already published configurations. The Poisson's ratio is varied in the full thermodynamically admissible range [−1.0, 0.5] and some quite peculiar results are found and explained, especially for disks made of auxetic materials, i.e. for ν<0. Although the stress fields are independent of the value of ν, the dependency of the critical load intensities is not simply proportional to the dependency of the plate's bending stiffness on ν, and the buckling modes show significant changes when ν is varied. The buckling factors for disks under tensile loading are by an order of magnitude larger than those for the compressed disks. Of course, also the buckling modes differ completely between compression and tension. Furthermore, the post-buckling behavior is qualitatively and quantitatively significantly different, too. The considerations and the achieved results are interesting for scientists working in the field of structural stability and for engineers in lightweight design of structures. Furthermore, there are applications in the design of sensors and actors as well as of flexible electronics. Since similar thin membrane structures appear in biological tissues, the paper might be interesting also for biologists.