Study of possible void nucleation and growth in solids in the framework of the Davis-Nadai deformation theory

In the framework of the Davis-Nadai deformation theory, we study the problem of a ball with a central cavity subjected to internal and external pressure. The solution is constructed in the reference configuration for the polynomial material deformation law with possible regard to matter conservation inside the cavity. The obtained solution is analyzed; it is mathematically proved that the limit load exists in the case of uniform compression, and a method for determining this load is given. It is also proved that a new void can be formed in a solid ball in the case of its extension, and the critical load of void formation is estimated. It is shown that the already existing spherical void cannot completely disappear under the action of external pressure (assuming that its shape is preserved and remaining in the framework of the continuity hypothesis).