Wiener-Hopf type models for cracks in dynamic elastic lattices

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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.