Designing necks and wrinkles in inflated auxetic membranes

TL;DR

This paper explores the design of inflatable auxetic membranes with controlled wrinkles and necks, combining analytical and numerical methods to understand and induce specific instabilities for applications like haptics.

Contribution

It introduces a novel analytical and computational framework for controlling localized instabilities in inflatable auxetic membranes, enabling pattern design and functional morphing.

Findings

Analytical proof that necks and wrinkles do not overlap in pressurized, axisymmetric membranes.

Finite Element simulations confirm the onset and control of wrinkles through material inhomogeneities.

Potential applications in tactile interfaces such as Braille reading and haptics.

Abstract

This article presents the potentiality of inflatable, functionally-graded auxetic membranes to produce wrinkles and necks. We obtain elastic instabilities at desired locations in axisymmetric membranes and with prescribed patterns in square membranes. First, we use an analytical approach to obtain a series of universal results providing insights into the formation of wrinkles and necks in inflated, axisymmetric membranes. For example, we prove analytically that necks and wrinkles may never overlap in pressurized, axially symmetric membranes. Second, we implement the relaxed strain energy of tension field theory into a Finite Element solver (COMSOL). By tuning spatial inhomogeneities of the material moduli, we corroborate our universal results, describe the onset of wrinkling in an averaged way, and also generate non-trivial instabilities at desired locations. This study on membranes with morphing or corrugation on demand has potential applications in Braille reading and haptics.