# Nonlinear elasticity of incompatible surface growth

## TL;DR

This paper extends the linear elasticity theory of incompatible surface growth to include nonlinear effects, revealing limitations of the linear model in describing confined growth and elastic instabilities in elastic solids.

## Contribution

It introduces a nonlinear elasticity framework for incompatible surface growth, addressing the shortcomings of previous linearized models.

## Key findings

- Linear theory cannot describe kinematically confined growth.
- Nonlinear effects are crucial for understanding growth-induced instabilities.
- The new model captures complex post-growth stress states.

## Abstract

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.