Gologanu, Leblond, Perrin, and Devaux (GLPD) developed a constitutive model for
ductile fracture for porous metals based on generalized continuum mechanics
assumptions. The model predicted with high accuracy ductile fracture process in porous
metals subjected to several complex loads. The GLDP model performances over its
competitors has attracted the attention of several authors who explored additional
capabilities of the model. This paper provides analytical solutions for the problem of a
porous hollow sphere subjected to hydrostatic loadings, the matrix of the hollow sphere
obeying the GLPD model. The exact solution for the expressions of the stress
and the generalized stress the GLPD model involved are illustrated for the case
where the matrix material does not contain any voids. The results show that the
singularities obtained in the stress distribution with the local Gurson model are
smoothed out, as expected with any generalized continuum model. The paper also
presents some elements of the analytical solution for the case where the matrix is
porous and obeys the full GLPD model at the initial time when the porosity is
fixed. The later analytical solution can serve to predict the mechanisms of ductile
fracture in porous ductile solids with two populations of cavities with different
sizes.