What is the bending rigidity of a book? Stacked plates as a dissipative structured beam

Multi-layered structures have long been exploited in engineering to design stiff and lightweight structural elements. For example, sandwich-structured composites involve an interplay between the mechanical properties of the individual layers and the inter-layer interactions through the matrix. In the absence of a matrix, when the layers are free to slide with respect to one another, energy is dissipated by frictional interactions. Here, in the context of designing high-performing metamaterial dampers, we focus on providing a quantitative description of the mechanical response of stacks composed of a large number (n~50) of elastic plates interacting through friction. In essence, we ask: “What is the bending rigidity of a book?” The mechanical response of our stacks is assessed experimentally through precision nonlinear bending tests. Naturally, our findings deviate from the purely linear elastic case, exhibiting surprising stiffening effects and hysteretic behavior. Taking friction as a perturbation, we develop a predictive model involving the coupling between the geometric nonlinearities, elasticity and friction that is in excellent agreement with experiments.