{"data":{"id":"10.6084/m9.figshare.c.3593549","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.3593549","prefix":"10.6084","suffix":"m9.figshare.c.3593549","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"A. Van Pamel","affiliation":[],"nameIdentifiers":[]},{"name":"G. Sha","affiliation":[],"nameIdentifiers":[]},{"name":"S. I. Rokhlin","affiliation":[],"nameIdentifiers":[]},{"name":"M. J. S. Lowe","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Supplementary material from \"Finite-element modelling of elastic wave propagation and scattering within heterogeneous media\""}],"publisher":"Figshare","container":{},"publicationYear":2016,"subjects":[{"subject":"Mechanical Engineering"},{"subject":"FOS: Mechanical engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Computational Physics"},{"subject":"20301 Acoustics and Acoustical Devices; Waves","subjectScheme":"FOR"},{"subject":"FOS: Physical sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2016-12-10","dateType":"Created"},{"date":"2016-12-10","dateType":"Updated"},{"date":"2016","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1098/rspa.2016.0738","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"https://creativecommons.org/licenses/by/4.0"}],"descriptions":[{"description":"The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two- or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The general methodology is described and further developed to enable the study of fundamental scattering behaviour in terms of the scattering induced attenuation and dispersion. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using an established Voronoi approach to randomly generate representative models. The numerically observed scattering behaviour is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/collections/Supplementary_material_from_Finite-element_modelling_of_elastic_wave_propagation_and_scattering_within_heterogeneous_media_/3593549","conten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