Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites

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This paper investigates the scaling from a statistical volume element (SVE; i.e. mesoscale level) to representative volume element (RVE; i.e. macroscale level) of spatially random linear viscoelasticmaterials, focusing on the quasi-static properties in the frequency domain. Requiring the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on the RVE response are developed from the Hill-Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The frequency and scale dependencies of mesoscale bounds are obtained through computational mechanics for composites with planar random chessboard microstructures. In general, the frequency-dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random chessboards and, essentially, is only a function of the microstructure and mesoscale.

Original languageEnglish (US)
Article number0801
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2188
StatePublished - Apr 1 2016


  • Mesoscale bounds
  • Random composite
  • Representative volume element
  • Scaling function
  • Viscoelasticity

ASJC Scopus subject areas

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


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