Electrical properties of random checkerboards at finite scales

Bharath V. Raghavan, Shivakumar I. Ranganathan, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


Under investigation is the scale dependent electrical conductivity (and resistivity) of two-phase random checkerboards at arbitrary volume fractions and phase contrasts. Using variational principles, rigorous mesoscale bounds are obtained on the electrical properties at finite scales by imposing a boundary condition that is either uniform electric potential or uniform current density. We demonstrate the convergence of these bounds to the effective properties with increasing length scales. This convergence gives rise to the notion of a scalar-valued scaling function that accounts for the statistical nature of the mesoscale responses. A semi-analytical closed form solution for the scaling function is obtained as a function of phase contrast, volume fraction and the mesoscale. Finally, a material scaling diagram is constructed with which the convergence to the effective properties can be assessed for any random checkerboard with arbitrary phase contrast and volume fraction.

Original languageEnglish (US)
Article number017131
JournalAIP Advances
Issue number1
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • General Physics and Astronomy


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