Negative Poisson's ratio is obtained by use of re-entrant cells; also via softening of bulk modulus during phase transformations. High ratio of strength to weight ratio is achieved in cellular solids by structural hierarchy. High stiffness combined with high damping obtained via inclusion shape guided by composite theory and use of materials with broadband damping. Extreme values of positive or negative thermal expansion occurs in designed lattices. These lattices exceed bounds by virtue of empty space or slip interfaces. Bounds have a tacit assumption of a perfect bond. Extreme values of stiffness and damping are achieved in composites with one constituent of negative stiffness (not positive definite), exceeding bounds based on positive definiteness. Sigmoid curves in modulus, a signature of negative stiffness, are observed in designed ceramic systems. Strain is redistributed in structured solids in accordance with Cosserat elasticity. This can be a pathway to enhanced toughness. |