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A theoretical framework in Lagrangian coordinates is developed for calculating the acoustic radiation force on an elastic sphere in a soft elastic medium. Advantages of using Lagrangian coordinates are that the surface of the sphere is fixed in the reference frame, and nonlinearity appears only in the stress tensor. The incident field is a time-harmonic compressional wave with arbitrary spatial structure, and there is no restriction on the size of the sphere. Bulk and shear viscosities are taken into account with complex wavenumbers. A solution is presented for the radiation force due to the scattered compressional wave. For an ideal liquid surrounding the sphere, there is no scattered shear wave contributing to the radiation force and the solution is complete. The theory reproduces established results obtained in Eulerian coordinates for an elastic sphere in a fluid.

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A theory for acoustic radiation force on a sphere in soft tissue was developed for arbitrary incident compressional wave fields [Ilinskii et al., Proc. Meet. Acoust. 19, 045004 (2013)]. This theory includes two contributions to the radiation force. The first depends only on the incident and scattered compressional waves, whereas the second depends on the scattered shear waves as well. Each contribution in turn has two parts, one due to direct integration of the time-averaged Piola-Kirchhoff stress tensor over the surface of the sphere, and the other due to the irrotational component of the body force on the sphere. While both parts are known analytically for the compressional waves, only the first part has been obtained analytically for the contribution involving shear waves. The irrotational portion associated with shear waves and its effect on the total radiation force is the subject of this presentation. The analysis is conducted via Helmholtz decomposition of the body force associated with shear waves and subsequent integration of the irrotational portion over the surface of the sphere. Simplifying analytical approximations based on numerical calculations are examined for various elastic properties of the sphere and soft tissue. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]