Negative stiffness induced by shear along wavy interfaces

Abstract

The extension of an elastic body almost always leads to mechanical tension in the stretching direction. Here, we report an unusual phenomenon of global mechanical compression in the stretching direction of an elastic body containing sinusoidal wavy interfaces. When the elastic body with a wavy interface is subjected to tensile loading, the local stress state along the interface is mixed-mode. Finite element simulations show that the resistance of the interface to shear-slip locks the interface together, and generates a moment couple which rotates the interface. Once the local adhesive shear strength of the interface is reached, the interface slips and separates. Then, the rotated interface triggers a restoring moment couple which releases the stored elastic energy. The structure subsequently undergoes global compression in the stretching direction until the interface completely separates. This moment-couple-induced internal energy storage and release mechanism leads to a material structure that exhibits high initial strength and toughness, followed by post-peak compliant softening with negative stiffness. This structural negative stiffness behavior is closely-tied with the ability of the interface to store and release energy by rotation, and is also exhibited by polycrystalline structures where grain rotation is possible.