Bending Response of a Book with Internal Friction

Area of Science:

• Physics
• Materials Science
• Mechanical Engineering

Background:

• Layered elastic systems exhibit complex behaviors due to interlayer interactions.
• Friction plays a critical role in the mechanical response of stacked materials.
• Understanding nonlinear elasticity and hysteresis is crucial for material design.

Purpose of the Study:

• To investigate the bending behavior of a booklike system composed of elastic plates.
• To develop a theoretical model for the nonlinear mechanical response of the layered system.
• To explore the potential of friction-induced energy dissipation for damping applications.

Main Methods:

• Experimental three-point bending tests on a stack of elastic plates.
• Dimensionality reduction to model the system as a nonlinear planar rod with internal shear.
• Perturbative treatment of interlayer friction and its coupling with nonlinear geometry.

Main Results:

• Observed nonadditive enhancement of apparent stiffness and significant hysteresis.
• Developed a centerline-based theory showing excellent agreement with experimental data.
• Rationalized energy dissipation over three orders of magnitude, including thick stack and large deflection regimes.

Conclusions:

• The developed model accurately predicts the mechanical response and dissipative behavior of the layered system.
• Interlayer friction is a key factor driving the system's rich mechanical properties.
• The robust dissipative mechanism offers potential for creating novel, efficient damping devices.