Competition between delamination and tearing in multiple peeling problems

Adhesive attachment systems consisting of multiple tapes or strands are commonly found in nature, for example in spider web anchorages or in mussel byssal threads, and their structure has been found to be ingeniously architected in order to optimize mechanical properties: in particular, to maximize dissipated energy before full detachment. These properties emerge from the complex interplay between mechanical and geometric parameters, including tape stiffness, adhesive energy, attached and detached lengths and peeling angles, which determine the occurrence of three main mechanisms: elastic deformation, interface delamination and tape fracture. In this paper, we introduce a formalism to evaluate the mechanical performance of multiple tape attachments in different parameter ranges, where an optimal (not maximal) adhesion energy emerges. We also introduce a numerical model to simulate the multiple peeling behaviour of complex structures, illustrating its predictions in the case of the staple-pin architecture. Finally, we present a proof-of-principle experiment to illustrate the predicted behaviour. We expect the presented formalism and the numerical model to provide important tools for the design of bioinspired adhesive systems with tuneable or optimized detachment properties.