Bending Response of a Book with Internal Friction

We study the bending of a booklike system, comprising a stack of elastic plates coupled through friction. The behavior of this layered system is rich and nontrivial, with a nonadditive enhancement of the apparent stiffness and a significant hysteretic response. A dimension reduction procedure is employed to develop a centerline-based theory describing the stack as a nonlinear planar rod with internal shear. We consider the coupling between the nonlinear geometry and the elasticity of the stacked plates, treating the interlayer friction perturbatively. This model yields predictions for the stack's mechanical response in three-point bending that are in excellent agreement with our experiments. Remarkably, we find that the energy dissipated during deformation can be rationalized over 3 orders of magnitude, including the regimes of a thick stack with large deflection. This robust dissipative mechanism could be harnessed to design new classes of low-cost and efficient damping devices.

Automated summary

The study focuses on the bending behavior of a booklike system made up of elastic plates, demonstrating nonadditive enhancement of stiffness and significant hysteresis. A dimension reduction procedure leads to a centerline-based theory describing the system's mechanical response. The energy dissipation during deformation can be rationally explained over three orders of magnitude, suggesting potential for designing new low-cost and efficient damping devices.