title: Finite-element modelling of elastic wave propagation and scattering within heterogeneous media.
abstract: 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 developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering 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.
authors.affiliation: Department of Mechanical Engineering , Imperial College London , Exhibition Road, London SW7 2AZ , UK.
authors.forename: A
authors.identifier: 0000-0002-9425-7522
authors.initials: A
authors.lastname: Van Pamel
authors.affiliation: Department of Materials Science and Engineering, Edison Joining Technology Center , The Ohio State University , 1248 Arthur E. Adams Drive, Columbus, OH 43221 , USA.
authors.forename: G
authors.initials: G
authors.lastname: Sha
authors.affiliation: Department of Materials Science and Engineering, Edison Joining Technology Center , The Ohio State University , 1248 Arthur E. Adams Drive, Columbus, OH 43221 , USA.
authors.forename: S I
authors.initials: SI
authors.lastname: Rokhlin
authors.affiliation: Department of Mechanical Engineering , Imperial College London , Exhibition Road, London SW7 2AZ , UK.
authors.forename: M J S
authors.initials: MJ
authors.lastname: Lowe
keywords: elastodynamics; heterogeneous media; stochastic finite elements; wave scattering