Tensor random fields in conductivity and classical or microcontinuum theories

Martin Ostoja-Starzewski, Lihua Shen, Anatoliy Malyarenko

Research output: Contribution to journalArticlepeer-review


We study the basic properties of tensor random fields (TRFs) of the wide-sense homogeneous and isotropic kind with generally anisotropic realizations. Working within the constraints of small strains, attention is given to antiplane elasticity, thermal conductivity, classical elasticity and micropolar elasticity, all in quasi-static settings albeit without making any specific statements about the Fourier and Hooke laws. The field equations (such as linear and angular momentum balances and strain-displacement relations) lead to consequences for the respective dependent fields involved. In effect, these consequences are restrictions on the admissible forms of the correlation functions describing the TRFs.

Original languageEnglish (US)
Pages (from-to)418-432
Number of pages15
JournalMathematics and Mechanics of Solids
Issue number4
StatePublished - Apr 4 2015


  • Elasticity
  • conductivity
  • correlation functions
  • fields
  • microcontinuum
  • tensor random

ASJC Scopus subject areas

  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials


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