Spectral and evolution analysis of composite elastic plates with high contrast

Kirill Cherednichenko, Marin Buzancic, Igor Velcic, Josip Zubrinic

Research output: Contribution to journalArticlepeer-review

Abstract

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
JournalJournal of Elasticity
Publication statusAcceptance date - 11 Nov 2022

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