  Surface growth is a crucial component of many natural and artificial
processes from cell proliferation to additive manufacturing. In elastic systems
surface growth is usually accompanied by the development of geometrical
incompatibility leading to residual stresses and triggering various
instabilities. In a recent paper (PRL, 119, 048001, 2017) we developed a
linearized elasticity theory of incompatible surface growth which
quantitatively linked deposition protocols with post-growth states of stress.
Here we extend this analysis to account for both physical and geometrical
nonlinearities of an elastic solid. The new development reveals the
shortcomings of the linearized theory, in particular, its inability to describe
kinematically confined surface growth and to account for growth-induced elastic
instabilities.
