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