Thermal expansion
Lakes, R. S., "Cellular solid structures with unbounded thermal expansion", Journal of Materials Science Letters, 15, 475-477 1996.
Material microstructures are presented which can exhibit coefficients of thermal expansion with a magnitude larger than that of either constituent. The thermal expansion can be either positive or negative depending on the lattice geometry. We conceptualize cellular solids as square (as shown in the image) or hexagonal lattices with two-layer rib elements and determine the thermal expansion coefficient. Thermal expansion increases without bound as the rib elements are made more slender. These cellular solids contain considerable void space. Colossal thermal expansion is possible. Get pdf .


Lakes, R. S., "Dense solid microstructures with unbounded thermal expansion", J. Mechanical Behav. Mts., 7, 85-92, 1996.
We present dense extremal structures which substantially exceed the bounds for thermal expansion of a two-phase composite, by allowing slip at interfaces between phases get pdf . New classes of extremal materials with extreme properties are envisaged, based on slip interfaces and void space tending to zero. Extremely high thermal expansion or negative thermal expansion is possible in these laminates.

Wang, Y. C. and Lakes, R. S., "Extreme thermal expansion, piezoelectricity, and other coupled field properties in composites with a negative stiffness phase", Journal of Applied Physics, 90, 6458-6465, Dec. (2001).
Particulate composites with negative stiffness inclusions in a viscoelastic matrix are shown to have higher thermal expansion than that of either constituent and exceeding conventional bounds. It is also shown theoretically that other extreme linear coupled field properties including piezoelectricity and pyroelectricity occur in layer- and fiber-type piezoelectric composites, due to negative inclusion stiffness effects. The causal mechanism is a greater deformation in and near the inclusions than the composite as a whole. A block of negative stiffness material is unstable, but negative stiffness inclusions in a composite can be stabilized by the surrounding matrix and can give rise to extreme viscoelastic effects in lumped and distributed composites. In contrast to prior proposed composites with unbounded thermal expansion, neither the assumptions of void spaces nor slip interfaces are required in the present analysis.
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Lakes, R. S., "Solids with tunable positive or negative thermal expansion of unbounded magnitude", Applied Phys. Lett. 90, 221905 (2007).
Material microstructures are presented with a coefficient of thermal expansion larger in magnitude than that of either constituent. Thermal expansion can be large positive, zero, or large negative. Three-dimensional lattices with void space exceed two-phase bounds but obey three-phase bounds. Lattices and normal materials have a trend of expansion decreasing with modulus. Two-phase composites with a negative stiffness phase exceed bounds that assume positive strain energy density. Young's modulus and its relation to thermal expansion are plotted; behavior of these composites is compared with that of homogeneous solids in expansion-modulus maps.
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