A theoretical-numerical model for the peeling of elastic membranes

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 theoretical-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.