Wiener-Hopf type models for cracks in dynamic elastic lattices

Lead Research Organisation: University of Liverpool
Department Name: Mathematical Sciences

Abstract

The project involves modelling of dynamic lattice structures with periodicallydistributed defects. Such a lattice may have non-trivial filtering/polarisationproperties. In particular, we are planning to consider cracks propagating in thediscrete inhomogeneous lattice structures and address the question of design of alattice that may stop (or deflect) dynamic cracks of a certain type. Fordynamic problems of elasticity, this is a challenging task. However, the background work of Prof Slepyan and of the proposers will enable us to make a good progress. We envisage new features of the lattice solutions that do not occur in the continuum models. Practical applications of this work are in the design of earthquake resistant structures.

Publications

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MISHURIS G (2008) Dynamical extraction of a single chain from a discrete lattice in Journal of the Mechanics and Physics of Solids

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Mishuris G (2007) Waves and fracture in an inhomogeneous lattice structure in Waves in Random and Complex Media

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Mishuris G (2008) Dynamics of a bridged crack in a discrete lattice in The Quarterly Journal of Mechanics and Applied Mathematics

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Movchan A (2007) Band gap Green's functions and localized oscillations in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences