A numerical model for the peeling of elastic membranes

TL;DR

This paper introduces a numerical model to simulate the peeling of elastic membranes from substrates, capturing complex two-dimensional adhesive behaviors to better understand biological attachment mechanisms.

Contribution

The paper develops a 3D numerical approach with a cohesive law to model membrane detachment, extending beyond traditional one-dimensional peeling models.

Findings

Pull-off force can be optimized by adjusting geometrical and mechanical parameters.

The length of the peeling boundary significantly influences adhesion strength.

The model aligns well with analytical results for simple geometries.

Abstract

The adhesive behaviour of biological attachment structures such as spider web anchorages is usually studied using single or multiple peeling models involving "tapes", i.e. one-dimensional contacts elements. This is an oversimplification for many practical problems, since the actual delamination process requires the modelling of complex two-dimensional adhesive elements. To achieve this, we develop a numerical approach to simulate the detachment of an elastic membrane of finite size from a substrate, using a 3D cohesive law. The model is validated using existing analytical results for simple geometries, and then applied in a series of parametric studies. Results show how the pull-off force can be tuned or optimized by varying different geometrical or mechanical parameters in various loading scenarios, and the length of the detachment boundary, known as the peeling line, emerges as the key factor to maximize adhesion. The approach presented here can allow a better understanding of the mechanical behaviour of biological adhesives with complex geometries or with material anisotropies, highlighting the interaction between the stress distributions at the interface and in the membrane itself.