Transition from equatorial to whole-shell buckling in embedded spherical shells under axisymmetric far-field loading

Motivated by the need to understand the compression of syntactic foam composites, we solve the canonical problem of buckling of a thin spherical shell embedded in a medium that is much softer than the shell. Syntactic foams comprise shells that usually have diameters in the micron range and are distributed inside a matrix medium that is typically polymeric. Such foams are commonly employed in a range of applications where high stiffness to density ratios are of interest. This can be tailored via choice of shell thickness and type, and filler volume fraction.