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We analyse the behaviour of thin composite plates whose material propertiesvary periodically in-plane and possess a high degree of contrast between theindividual components. Starting from the equations of three-dimensional linearelasticity that describe soft inclusions embedded in a relatively stiffthin-plate matrix, we derive the corresponding asymptotically equivalenttwo-dimensional plate equations. Our approach is based on recent resultsconcerning decomposition of deformations with bounded scaled symmetrisedgradients. Using an operator-theoretic approach, we calculate the limitresolvent and analyse the associated limit spectrum and effective evolutionequations. We obtain our results under various asymptotic relations between thesize of the soft inclusions (equivalently, the period) and the plate thicknessas well as under various scaling combinations between the contrast, spectrum,and time. In particular, we demonstrate significant qualitative differencesbetween the asymptotic models obtained in different regimes.

Spectral and evolution analysis of composite elastic plates with high contrast