Scattering of elastic waves by a sphere with orthorhombic anisotropy and application to polycrystalline material characterization
Journal article, 2024

Scattering of elastic waves by an anisotropic sphere with orthorhombic symmetry inside an isotropic medium is studied and applied to characterization of polycrystalline materials with anisotropic grains. For a single sphere the waves in the isotropic surrounding are expanded in the spherical vector wave functions. Inside the sphere, the elastodynamic equations are first transformed to spherical coordinates and the displacement field is expanded in terms of the vector spherical harmonics in the angular directions and power series in the radial direction. The governing equations inside the sphere give recursion relations among the expansion coefficients in the power series. The boundary conditions on the sphere then determine the relation among the scattered wave expansion coefficients and those of the incident wave, expressed as the transition (T) matrix. For low frequencies the elements of the T matrix are obtained in explicit form. According to the theory of Foldy the T matrix elements of a single sphere are used to study attenuation and phase velocity of polycrystalline materials, explicitly for low frequencies. Comparisons of the present method with previously published results and recent FEM results show a good correspondence for low frequencies. The present approach shows a better agreement with FEM for strongly anisotropic materials in comparison with other published methods.

Polycrystal

Elastic wave scattering

Effective wave number

Spherical inclusion

Orthorhombic anisotropy

Author

Ata Jafarzadeh

Chalmers, Mechanics and Maritime Sciences (M2), Dynamics

Peter Folkow

Chalmers, Mechanics and Maritime Sciences (M2), Dynamics

Anders E Boström

Chalmers, Mechanics and Maritime Sciences (M2), Dynamics

Ultrasonics

0041-624X (ISSN)

Vol. 138 107199

Scattering of elastic waves in anisotropic media

Swedish Research Council (VR) (2017-03958), 2018-01-01 -- 2021-12-31.

Subject Categories

Applied Mechanics

Other Electrical Engineering, Electronic Engineering, Information Engineering

Condensed Matter Physics

DOI

10.1016/j.ultras.2023.107199

PubMed

38016389

Related datasets

Scattering of elastic waves by a sphere with orthorhombic anisotropy and application to polycrystalline material characterization-Supplementary Documents [dataset]

URI: https://figshare.com/s/5b839532ebfee747830f

More information

Latest update

1/7/2024 2