The effective compressibility of a hollow sphere

Abstract

The problem of determining the effective compressibility of a hollow sphere is practically important because it relates to the problem of compacting a real material containing voids. For example, the void content in propellants is such that the initial slope of the P-V curve is three-to-ten times lower than the limiting slope obtained after all the voids have been collapsed. The phenomenon of compaction-decompaction is extremely important in determining the mechanical properties of propellants since it accounts for much of the batch-to-batch variability and also is a function of the stress-time-temperature history of the material. In this memo we consider only a very special type of compaction, but it is believed that this will pave the way for further analysis along these lines.