Extreme Damping in Composite Materials with a Negative Stiffness Phase

Composites with negative stiffness inclusions in a viscoelastic matrix are shown to have higher stiffness and mechanical damping $\tan \delta$ than that of either constituent and exceeding conventional bounds. The causal mechanism is a greater deformation in and near the inclusions than the composite as a whole. Though a block of negative stiffness is unstable, negative stiffness inclusions in a composite can be stabilized by the surrounding matrix. Such inclusions may be made from single domains of ferroelastic material below its phase transition temperature or from prebuckled lumped elements.