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

Abstract

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.]