### ASA 124th Meeting New Orleans 1992 October

## 3pSA13. Effective material properties of a hollow elastic sphere that
undergoes a finite deformation under the action of external hydrostatic
pressure.

**Anthony J. Rudgers
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*Naval Res. Lab., Underwater Sound Reference Detachment, P.O. Box 568337,
Orlando, FL 32856-8337
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The analytic solution to the problem of the linear, but finite,
deformation of a hollow elastic sphere, occurring when the sphere is subject to
external hydrostatic pressure, is described in this paper. In this problem, the
theory of linear elasticity is considered to characterize incremental
deformation of the hollow sphere, but, owing to the concomitant incremental
change in geometry, the radial deformation of the sphere caused by a
hydrostatic pressure of finite magnitude is a nonlinear function of that
pressure. By calculating how a hollow sphere deforms with pressure, the
effective bulk modulus and effective density of the sphere can be found as a
function of hydrostatic pressure. These effective properties of hollow spheres
would be needed if one wished to describe the acoustic behavior of
syntactic-foam composite materials that incorporate hollow spheres as one of
their constituents. [Work supported by ONR.]