A failure condition recently proposed for the composite material syntactic foam is applied to the inhomogeneous state of stress which occurs in a layered sphere exposed to external pressure. The sphere is composed of syntactic foam which surrounds an assumed perfectly elastic hollow inclusion of higher strength than the syntactic foam. In addition to the establishment of the stress level at which the syntactic foam begins to crush, an analysis similar to that of perfect plasticity theory is carried out to find the ultimate collapse pressure of the syntactic foam. The results are found to compare favorably with experimental data. This problem is of importance in the further development of buoyancy materials for deep submergence vehicles.

An analysis of bending stresses in flexible cables has been carried out. It has been found that stresses which arise due to fixity at the boundaries or other points of discontinuity, decay in an exponential manner from such boundaries, similar to the edge effect solutions of shell theory. Such a phenomenon makes it possible to analyze a finite cable of sufficient length using solutions which are applicable only to infinite or very long cables. In this way the cumbersome but otherwise exact solutions of the elastica are replaced by much simpler ones of sufficient engineering accuracy. The term “sufficient length” is defined as part of the analysis.

A failure condition is proposed for the composite material “syntactic foam” based upon an experimental program carried out under combined biaxial and triaxial stress states. The material itself is composed of hollow glass “microspheres” embedded in an epoxy resin matrix. It exhibits finite strength under hydrostatic compression, unlike any other engineering material and thus gives rise to a closed failure surface in principal stress space. In addition to loadings corresponding to radial lines starting from the origin in stress space out to the failure envelope, other load paths were also used. Some effects due to loading and unloading and then reloading to another stress state were also investigated. Under biaxial stress states it was found that the ultimate strength of the material is sensitive to its past stress history to some degree, the reason being attributed to the initially isotropic material developing weak planes perpendicular to the compressive principal stress resulting in a “latent anisotropy.”