The theory of multiple peeling

In this paper we derive the theory of multiple peeling, extending the pioneering energy-based single peeling theory of Kendall, including large deformations and pre-stretching. We can thus treat a complex system of films, adhering over a substrate and having a common hinge where the pulling force is applied. Two case studies are investigated: the asymmetric V-shape double peeling and the symmetric cone-shape configuration with N peeling tapes, both requiring the solution of six nonlinear coupled equations (instead of the one needed in the simpler single peeling problem). Remarkable implications emerge: (1) for moderate deformations, the critical strain of a tape is identical to that of the single peeling; (2) an optimal peeling angle, at which adhesion is maximal, is discovered; (3) an additional optimization, even for hierarchical structures, is introduced by imposing the delamination force equal to the intrinsic fracture of the tape. Also, the length of the peeling process zone is calculated, suggesting different optimal values for flaw-tolerant peeling at different angles. Applications to gecko adhesion, for which the flaw-tolerant peeling is demonstrated, and spider silk anchors, that we are going to discuss in details in subsequent papers, are envisioned (including a new pre-stretching mechanism for adhesion control) and suggested by the evidence of a smart mechanism capable of maximizing adhesion simply by increasing the applied tension.