Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks

Ran Li, Seyedsajad Moazzeni, Liping Liu, Hao Lin

Research output: Contribution to journalArticlepeer-review


We demonstrate that for a rigid and incompressible network in mechanical equilibrium, the microscopic stress and strain follows a simple relation, σ=pE, where σ is the deviatoric stress, E is a mean-field strain tensor, and p is the hydrostatic pressure. This relationship arises as the natural consequence of energy minimization or equivalently, mechanical equilibration. The result suggests not only that the microscopic stress and strain are aligned in the principal directions, but also microscopic deformations are predominantly affine. The relationship holds true regardless of the different (foam or tissue) energy model considered, and directly leads to a simple prediction for the shear modulus, μ=«p»/2, where «p» is the mean pressure of the tessellation, for general randomized lattices.

Original languageEnglish (US)
Article number188201
JournalPhysical review letters
Issue number18
StatePublished - May 5 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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