Generalized multiple peeling theory uploading hyperelasticity and pre-stress

Extreme adhesion mechanisms are shown in a wide number of situations in nature, from structures of single cells and spider web anchorages to hierarchical organization of ends and pads of insects and reptiles. With this in mind, we here propose a general formulation of multiple peeling theory accounting for geometrical and constitutive nonlinearities, i.e. large deformations and hyperelasticity. Pre-stress of adherent tracts and different initial V-shaped configurations of the tapes have been also included in the modelling. By following an analytical approach, closed-form solutions and explicit formulas were given for predicting pull-off critical forces and optimality conditions maximizing the adhesion strength, as well as for tracing the evolution of the delamination process, from the detaching onset to its progressive behaviour. Kendall and previous constitutively linear multiple peeling theory approaches were all recovered as limit cases, gaining insights into the role played by nonlinearities and pre-stress and also demonstrating – with mathematically rigorous arguments – the asymptotic character of the detaching phenomenon observed experimentally. Example applications and simple key tests were provided to show the effectiveness of the approach, which could help to interpret peeling in nature and to design materials with enhanced adhesive properties.