  Residual stresses may appear in elastic bodies due to the formation of
misfits in the micro-structure, driven by plastic deformations, thermal or
growth processes. They are especially widespread in living matter, resulting
from the dynamic remodelling processes aiming at optimizing the overall
structural response to environmental physical forces. From a mechanical
viewpoint, residual stresses are classically modelled through the introduction
of a virtual incompatible state that collects the local relaxed states around
each material point. In this work, we instead employ an alternative approach
based on a strain energy function that constitutively depends only on the
deformation gradient and the residual stress tensor. In particular, our
objective is to study the morphological stability of an incompressible sphere,
made of a neo-Hookean material and subjected to given distributions of residual
stresses. Firstly, we perform a linear stability analysis on the pre-stressed
solid sphere using the method of incremental deformations. The marginal
stability conditions are given as a function of a control parameter, being the
dimensionless variable that represents the characteristic intensity of the
residual stresses. Secondly, we perform finite element simulations using a
mixed formulation in order to investigate the post-buckling morphology in the
fully nonlinear regime. Considering different distributions of the residual
stresses, we find that different morphological transitions occur around the
material domain where the hoop residual stress reaches its maximum compressive
value. The results provide useful guidelines in order to design morphable soft
spheres, for example by controlling the residual stresses through active
deformations. They finally suggest a viable solution for the nondestructive
characterization of residual stresses in soft tissues, such as solid tumors.
