Peeling under large bending deformations: Follower versus fixed loads. A unified approach for concentrated or distributed loads. (1st April 2022) - Barbieri, Ettore; Botto, Lorenzo
Abstract: In the non-dissipative regime, the potential energy is the difference between the strain energy of the deforming solid and the work done by the external forces. For configuration-dependent external forces, whose direction is perpendicular to the deformed shape, we obtain a simple formula for the strain energy release rate of peeled strips experiencing large deformations and prove rigorously that the same formula applies for external forces having fixed direction. We then apply Griffith's criterion for fracture to calculate critical loads for two cases: peeling produced by a uniform follower pressure distributed along the flexible strip and peeling produced by a localized follower shear force applied at the edge of the strip. We found that for these loads, the critical pressure for peeling follows approximately q c ∼ Γ L − 1, where Γ is the solid–solid interface energy and L is the initial peeling length; for the shear force, the corresponding critical value instead follows Q 0 c ∼ Γ, independently of the initial length. These formulas are, unexpectedly, independent of the bending stiffness E I of the strips and differ from the ones predicted for small deformations, i.e. q c ∝ L − 2 E I Γ and Q 0 c ∝ L − 1 E I Γ . We apply our results to predict the critical hydrodynamic load necessary to exfoliate graphene sheets from graphite, a fluid–structure interaction problem where the load is of the follower type. We find that a follower load peeling model gives significantly improved predictions than fixed load peeling. For the same Γ, L and b, the critical hydrodynamic follower load is always lower than the one with fixed forces: approximately half for the case with uniform pressure, and one third for the case with shear force.