Nonlinear elasticity of incompatible surface growth

In this manuscript with Lev Truskinovsky, we developed a new nonlinear theory of large-strain incompatible surface growth. 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. Here we developed a nonlinear theory of incompatible surface growth which quantitatively linkes deposition protocols with post-growth states of stress. Our analysis accounts for both physical and geometrical nonlinearities of an elastic solid and 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. We illustrated the general theory by a series of examples emphasizing the role of finite strains in the surface growth of soft solids. Through these examples we showed that geometrical frustration developing during deposition can be indeed fine-tuned and that such 'information rich' solids can be designed to undergo specific elastic instabilities, and to exhibit specific patterning in the technologically relevant conditions.