An exact analytical solution for stress concentrations within layered hollow spheres under compression

The paper presents the exact analytical solution for the stress concentrations within a layered hollow sphere under diametral compression. Numerical results show that the stress distribution within a layered hollow sphere changes drastically along the axis of loading, and the maximum tensile hoop stress may appear at the interface as well as at the internal surface. In general, a harder outer layer leads to a maximum tensile hoop stress in the outer layer near the interface; whereas a softer outer layer leads to a compressive hoop stress at the same location. A thinner outer layer usually results in a higher tensile hoop stress, regardless of the relative stiffness between the layer and the hollow sphere. The hoop stress at the interface also increases with the internal pressure but decreases with the contact size of loading. By changing the relative thickness and mechanical properties of the layered hollow sphere, the present solution not only provides the basis for the design and the fabrication of suitable layered hollow spheres with multiple functions against delamination at the interfaces or tensile cracking at the internal surfaces, but also provides a useful benchmark for the numerical simulations for various advanced multilayered hollow spheres.