PhD Thesis Proposals

Phase-field modeling of surface growth coupled with diffusion and its stability analysis

Motivation

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:

In all these cases, the formation of a new material surface is strongly dependent on chemo-mechanically coupled processes that occur within the material, which may involve thermal or diffusion effects.

Surface growth may induce mechanical instability, which plays a crucial role in morphogenesis. Most descriptions of growth-induced instability are concerned with a prescribed growth path.

Question

Suppose that we are working with a diffuse interface model. Then the question is: what is the extension of the body?

We write the stress work as:

\[\int_{\text{Space}} \varphi N \delta \varepsilon\]

or as:

\[\int_{\text{Space}} N \delta \varepsilon\]

The constitutive equation would be:

\[N = \mathbb{C}(c) \varepsilon\]

where $c$ is the concentration of solvent.

References