Rod Lakes, lakes@engr.wisc.edu
Extreme elastic, viscoelastic and piezoelectric properties in structured materials
Materials with extremely high, even singular values of physical properties, are developed. Materials with
designed heterogeneity including inclusions of negative compressibility can exhibit extremely high values of
viscoelastic damping approaching a singularity, high Young’s modulus (even greater than that of diamond) or
piezoelectric sensitivity. Such behavior exceeds the usual theoretical bounds. The reason is that assumptions
made in deriving the bounds can be relaxed in certain materials and microstructures. We consider toughness
in the context of Cosserat elasticity in which there are characteristic lengths as additional engineering elastic
constants. There are a total of six independent elastic constants in an isotropic Cosserat solid. Experimental
work discloses a variety of cellular and fibrous materials to exhibit such freedom, and the characteristic lengths
have been measured. In selected isotropic cellular solids all six of the Cosserat elastic constants have been
measured. Several of these constants have been verified by further experiments in geometries different from
those used in the original measurements. Holographic studies show that strain can spill over into regions which
are classically forbidden, specifically the corners of a square cross-section prism in torsion.