Nonlinear elasticity of incompatible surface growth

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.

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• Mechanical Feedback in Regulating the Size of Growing Multicellular Spheroids
• Surface tension-driven boundary growth in tumour spheroids
• A continuum model for the growth of dendritic actin networks
• Geometrical dynamics of edge-driven surface growth