Effective mechanical and transport properties of cellular solids

S. Torquato, L. V. Gibiansky, M. J. Silva, L. J. Gibson

Research output: Contribution to journalArticlepeer-review

181 Scopus citations


We utilize two different approaches, homogenization theory and discrete network analyses, to study the mechanical and transport properties of two-dimensional cellular solids (honeycombs) consisting of either hexagonal, 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 honeycombs in terms of the elastic moduli and vice versa. It is shown that for hexagonal, triangular or square honeycombs, the cross-property bound relating the bulk modulus to the thermal conductivity turns out to be an exact and optimal result. The same is true for the cross-property bound linking the shear or Young's modulus of the triangular honeycomb 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 the low-density limit are proportional to the complex Young's modulus of the solid phase. Such structures have real Poisson's ratios and the loss tangent is the same for any load.

Original languageEnglish (US)
Pages (from-to)71-82
Number of pages12
JournalInternational Journal of Mechanical Sciences
Issue number1
StatePublished - Jan 1998

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • General Materials Science
  • Civil and Structural Engineering


  • Cellular solids
  • Composites
  • Elasticity
  • Viscoelasticity


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