Locally-periodic homogenization and plywood microstructures

Mariya Ptashnyk (University of Dundee)

Thursday 25th October, 2012 14:00-15:00 325


Many biological or industrial composite materials comprise non-periodic microscopic structures, for example fibrous microstructure with varied orientation of fibres in exoskeletons, in polymer membranes and in industrial filters, or space-dependent perforations in concrete. An interesting and important for applications special case of non-periodic microstructures is so called locally-periodic microstructure, where spacial changes of the microstructure are observed on the scale smaller than the size of the considered domain but larger than the characteristic size of the microstructure. Thus the generalisation of the homogenization technique of two-scale convergence, widely used for the multiscale analysis of PDEs posed in domains with periodic microstructures, to locally-periodic situations is proposed. The developed theory is applied to derive effective macroscopic equations for a linear elasticity problem defined in a domain with a plywood structure, characterised by the superposition of gradually rotated planes of parallel aligned fibres.

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