Boundary conditions for macroscale waves in an elastic system with microscale heterogeneity

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dc.contributor.authorChen, C.
dc.contributor.authorRoberts, A.J.
dc.contributor.authorBunder, J.E.
dc.date.issued2018
dc.descriptionAdvance Access Publication on 19 March 2018
dc.description.abstractMultiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments, potentially resulting in a macroscale model which fails to adequately capture the behaviour of the microscale system. We derive the macroscale boundary conditions of the macroscale model for longitudinal wave propagation on a lattice with periodically varying density and elasticity. We model the macroscale dynamics of the microscale Dirichlet, Robin-like, Cauchy-like and mixed boundary value problem. Numerical experiments test the new methodology. Our method of deriving boundary conditions significantly improves the accuracy of the macroscale models. The methodology developed here can be adapted to a wide range of multiscale wave propagation problems
dc.description.statementofresponsibilityChen Chen, A. J. Roberts and J. E. Bunder
dc.identifier.citationIMA Journal of Applied Mathematics, 2018; 83(3):347-379
dc.identifier.doi10.1093/imamat/hxy004
dc.identifier.issn0272-4960
dc.identifier.issn1464-3634
dc.identifier.orcidRoberts, A.J. [0000-0001-8930-1552]
dc.identifier.orcidBunder, J.E. [0000-0001-5355-2288]
dc.identifier.urihttp://hdl.handle.net/2440/124089
dc.language.isoen
dc.publisherOxford University Press (OUP)
dc.rights© The Author(s) 2018. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
dc.source.urihttps://doi.org/10.1093/imamat/hxy004
dc.subjectmicro; macro; multiscale; boundary condition; wave; centre manifold; macroscale modelling; heterogeneity; heterogeneous models
dc.titleBoundary conditions for macroscale waves in an elastic system with microscale heterogeneity
dc.typeJournal article
pubs.publication-statusPublished

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