Multi-scale modelling of nano- and meta materials

We carry out research in the mathematics and mechanics of nano- and meta-materials; strongly inhomogeneous micro-structured solids.

Many modern high-tech domains are concerned with a variety of multi-scale phenomena, containing diverse space and temporal sizes, including nano-, micro-, meso- and macroscales. An asymptotic approach is the main tool for tackling emerging mathematical problems formulated in terms of continuum or lattice mechanics.

The general methodology in multi-scale modelling naturally develops the previous efforts within a more classical framework. In particular, high-frequency homogenisation procedures for periodic media originate from former asymptotic considerations for elastic plates and shells. Boundary layers, localised near the borders of non-locally elastic solids have a similarity with those near the edges of thin structures. The powerful semi-membrane theory for thin elastic shells finds interesting applications in the modelling of elongated carbon nano-tubes. In addition, more recent fundamental developments for Rayleigh and Rayleigh-type waves has resulted in novel formulations for seismic meta-surfaces, including the bending ones. High-contrast multi-layered and multi-span elastic structures is another active area of the group.

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