Programmable wrinkling for functionally-graded auxetic circular membranes

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 ondemand in auxetic membranes, our study also confirms the potential of using tension field theory to study, analytically and numerically, instabilities in functionally graded materials.& COPY; 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

Materials with negative Poisson's ratio, known as auxetic materials, have unique properties of expansion in all directions under uni-axial tension. These materials have a wide range of applications in various fields. This study focuses on the wrinkling behavior of thin and soft auxetic membranes under edge tractions. The research reveals the non-trivial wrinkling patterns that can occur and disappear as the applied tractions increase, and proposes a mathematical method to model the wrinkling using tension field theory.