Mesoscale bounds in finite elasticity and thermoelasticity of random composites

Z. F. Khisaeva, M. Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


Under consideration is the problem of size and response of the Representative Volume Element (RVE) in the setting of finite elasticity of statistically homogeneous and ergodic random microstructures. Through the application of variational principles, a scale dependent hierarchy of strain energy functions (i.e. mesoscale bounds) is derived for the effective strain energy function of the RVE. In order to account for thermoelastic effects, the variational principles are first generalized, and then analogous bounds on the effective thermoelastic response are derived. It is also shown that, in contradiction to results obtained for random linear composites, the hierarchy on the effective strain energy function in nonlinear elasticity cannot be split into volumetric and isochoric terms, while the hierarchy on the effective free energy function cannot be divided into purely mechanical and thermal contributions.

Original languageEnglish (US)
Pages (from-to)1167-1180
Number of pages14
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2068
StatePublished - 2006


  • Finite elasticity
  • Finite thermoelasticity
  • Mesoscale bounds
  • Random composites
  • Representative volume element

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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