EFFECTIVE MECHANICAL AND TRANSPORT-PROPERTIES OF CELLULAR SOLIDS

We utilize two different approaches, homogenization theory and discret e network analyses, to study the mechanical and transport properties o f two-dimensional cellular solids (honeycombs) consisting of either he xagonal, triangular, square or Voronoi cells. We exploit results from homogenization theory for porous solids (in the low-density limit) to establish rigorous bounds on the effective thermal conductivity of hon eycombs in terms of the elastic moduli and vice versa. It is shown tha t for hexagonal, triangular or square honeycombs, the cross-property b ound relating the bulk modulus to the thermal conductivity turns out t o be an exact and optimal result. The same is true for the cross-prope rty bound linking the shear or Young's modulus of the triangular honey comb to its conductivity. For low-density honeycombs, we observe that all of the elastic moduli do not depend on the Poisson's ratio of the solid phase. The elastic-viscoelastic correspondence principle enables us to conclude that all of the viscoelastic moduli of honeycombs in t he low-density limit are proportional to the complex Young's modulus o f the solid phase. Such structures have real Poisson's ratios and the loss tangent is the same for any load. (C) 1997 Published by Elsevier Science Ltd.