Avoiding localization instabilities in rotary pleating

TL;DR

This paper models rotary pleating as a nonlinear boundary value problem to analyze how geometric and material parameters influence the stability and failure modes, such as kink formation and localization instability, in the pleating process.

Contribution

It introduces a novel boundary value problem formulation for rotary pleating, exploring multiple equilibria and failure conditions through numerical continuation, and identifies key parameters affecting process success.

Findings

Presence of stable kinked equilibria indicating potential failure

Successful pleating depends mainly on the distance from injection point to pack

Crease stiffness and strength influence process stability

Abstract

Rotary pleating is a widely used process for making filters out of nonwoven fabric sheets. This involves indirect elastic-plastic bending of pre-weakened creases by continuously injecting material into an accordion-shaped pack. This step can fail through a localization instability that creates a kink in a pleat facet instead of in the desired crease location. In the present work, we consider the effects of geometric and material parameters on the rotary pleating process. We formulate the process as a multi-point variable-arc-length boundary value problem for planar inextensible rods, with hinge connections. Both the facets (rods) and creases (hinges) obey nonlinear moment-curvature or moment-angle constitutive laws. Some unexpected aspects of the sleeve boundary condition at the point of material injection, common to many continuous sheet processes, are noted. The process, modeled as quasistatic, features multiple equilibria which we explore by numerical continuation. The presence of, presumably stable, kinked equilibria is taken as a conservative sign of potential pleating failure. Failure may also occur due to localization at the injection point. We may thus obtain "pleatability surfaces" that separate the parameter space into regions where mechanical pleating will succeed or fail. Successful pleating depends primarily on the distance between the injection point and the pleated pack. Other factors, such as the crease stiffness and strength relative to that of the facets, also have an influence. Our approach can be adapted to study other pleating and forming processes, the deployment and collapse of folded structures, or multi-stability in compliant structures.