Programmable wrinkling for functionally-graded auxetic circular membranes

TL;DR

This paper explores how spatially varying properties in auxetic membranes can be used to control complex wrinkling patterns, employing tension field theory for modeling and revealing new possibilities for on-demand surface patterning.

Contribution

It introduces a method to tailor wrinkling patterns in functionally graded auxetic membranes using tension field theory, enabling controlled and reversible surface morphologies.

Findings

Spatial inhomogeneities produce complex wrinkling patterns.

Tension field theory effectively models wrinkling in graded membranes.

Wrinkling patterns can be dynamically controlled by applied traction.

Abstract

Materials with negative Poisson's ratio, also known as auxetic materials, display exotic properties such as expansion in all directions under uni-axial tension. For their unique properties, these materials find a broad range of applications in robotic, structural, aerospace, and biomedical engineering. In this work we study the wrinkling behavior of thin and soft auxetic membranes, subjected to edge tractions. We show that spatial inhomogeneities of the Young modulus and of the Poisson ratio can be suitably tailored to produce non-trivial wrinkling patterns, with wrinkled regions that can appear, broaden, merge, and eventually disappear again, as the magnitude of applied tractions is increased monotonically. To model wrinkling in a functionally graded membrane, we employ the mathematically elegant and physically transparent tension field theory, an approximated method that we implement in commercially available software. Beyond unveiling the challenging technological potential to achieve non-standard wrinkling on-demand in auxetic membranes, our study also confirms the potential of using tension field theory to study, analytically and numerically, instabilities in functionally graded materials.