The Mullins effect in the wrinkling behavior of highly stretched thin films

TL;DR

This paper models the complex wrinkling behavior of highly stretched thin films, incorporating nonlinear elasticity and residual strains to predict phenomena like isola-center bifurcation and cyclic wrinkling patterns.

Contribution

It introduces a simple pseudo-elastic model that captures stress softening, residual strains, and cyclic wrinkling behavior, aligning with experimental observations.

Findings

Predicts isola-center bifurcation in wrinkling behavior

Models cyclic appearance and disappearance of wrinkles

Accurately describes first loading versus cyclic loading differences

Abstract

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading.