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Abstract
We analyse a problem of twodimensional linearised elasticity for a twocomponent periodic composite, where one of the components consists of disjoint soft inclusions embedded in a rigid framework. We consider the case when the contrast between the elastic properties of the framework and the inclusions, as well as the ratio between the period of the composite and the framework thickness increase as the period of the composite becomes smaller. We show that in this regime the elastic displacement converges to the solution of a special twoscale homogenised problem, where the microscopic displacement of the framework is coupled both to the slowlyvarying “macroscopic” part of the solution and to the displacement of the inclusions. We prove the convergence of the spectra of the corresponding elasticity operators to the spectrum of the homogenised operator, which has a bandgap structure.
Original language  English 

Pages (fromto)  658679 
Number of pages  22 
Journal  Journal of Mathematical Analysis and Applications 
Volume  473 
Issue number  2 
Early online date  11 Dec 2018 
DOIs  
Publication status  Published  15 May 2019 
Keywords
 Bandgap spectrum
 Highcontrast composites
 Loss of uniform ellipticity
 Periodic homogenisation
 Thin structures
 Twoscale convergence
ASJC Scopus subject areas
 Analysis
 Applied Mathematics
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Dive into the research topics of 'Homogenisation of thin periodic frameworks with highcontrast inclusions'. Together they form a unique fingerprint.Projects
 1 Finished

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council