Spectral and evolution analysis of composite elastic plates with high contrast

Marin Buzancic, Kirill Cherednichenko, Igor Velcic, Josip Zubrinic

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1 Citation (SciVal)


We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree of contrast between the individual components. Starting from the equations of threedimensional linear elasticity that describe soft inclusions embedded in a relatively stiff thin-plate matrix, we derive the corresponding asymptotically equivalent two-dimensional plate equations. Our approach is based on recent results concerning decomposition of deformations with bounded scaled symmetrised gradients. Using an operator-theoretic approach, we calculate the limit resolvent and analyse the associated limit spectrum and effective evolution equations. We obtain our results under various asymptotic relations between the size of the soft inclusions (equivalently, the period) and the plate thickness as well as under various scaling combinations between the contrast, spectrum, and time. In particular, we demonstrate significant qualitative differences between the asymptotic models obtained in different regimes.
Original languageEnglish
Pages (from-to)79-177
Number of pages99
JournalJournal of Elasticity
Issue number1-2
Early online date30 Nov 2022
Publication statusPublished - 1 Dec 2022


  • Dimension reduction
  • Effective media
  • High-contrast composites
  • Homogenisation
  • Resolvent convergence
  • Spectrum
  • Time evolution

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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