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 [G. Zurlo and L. Truskinovsky, Phys. Rev. Lett. 119, 048001 (2017)] we presented a linearized elasticity theory of incompatible surface growth, which provides a quantitative link between deposition protocols and postgrowth states of stress. Here we extend this analysis to account for both physical and geometrical nonlinearities of an elastic solid. This 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.

• Received 18 January 2019

DOI:https://doi.org/10.1103/PhysRevE.99.053001