Surface growth, i.e. the accretion of a solid onto a surface, occurs in several contexts of physical, technological, and biological interest. Conventional areas of application are
Solidification processes
3D printing
In all these case the formation of a new material surface is strongly dependent chemo-mechanically coupled processes that occur within the material, which may involve thermal or diffusion effects.
Surface growth body may induce mechanical instability, which play a crucial role in morphogenesis. Most description of growth-induces are concerned with a prescribed growth path, so that instability can
The theoretical description of growth
Question:
Suppose that we are working with the diffuse interface model. Then the question is:
what is the extension of the body?
We write the stress work as \[ \int_{\rm Space} \varphi N\delta\varepsilon \] or as \[ \int_{\rm Space} N\delta\varepsilon \]
The constitutive equation would be \[ N=\mathbb C(c)\varepsilon \] where \(c\) is the concentration of solvent.